Rational expressions - transformations and proofs

The database of the EMTeachline Mathematics Software contains approximately 5 000 000 of math problems. Math problems are graded in 11 difficulty classes and cover all skill levels from basic through advanced. The software modules are organized by subject. Covered subject areas are Arithmetic, Pre-algebra, Algebra I and II, Trigonometry and Hyperbolic Trigonometry. The Arithmetic and Pre-Algebra modules offer tasks on simplification and evaluation of numeric expressions, including fractional expressions, computational problems, proofs of numeric equalities. The Algebra modules offer simplification and evaluation problems, proofs of algebraic identities and inequalities, solutions of algebraic equations and inequalities; included are linear, quadratic, cubic, reciprocal, biquadratic and fractional expressions. The Trigonometry and Hyperbolic Trigonometry modules offer simplification and evaluation problems, proofs of trigonometric and hyperbolic identities, and solutions of trigonometric and hyperbolic equations; included are all the basic and inverse trigonometric and hyperbolic functions. All problems are solved or proved in full detail. Each module allows employing the database for development of math tests, quizzes, exams, revision exercises and homeworks. Currently available themes, chapters and sections, together with those in preparation, are listed below. Our free online demos allow viewing math examples online.

• Transformation of linear expressions and expressions reduced to them.Elementary linear expressions

• Transformation of linear expressions and expressions reduced to them.Elementary linear expressions containing fractions

• Transformation of linear expressions and expressions reduced to them.Linear expressions. Distributive law

• Transformation of linear expressions and expressions reduced to them.Linear expressions. Formulas of short multiplication

• Transformation of linear expressions and expressions reduced to them.Linear expressions. Formulas of short multiplication. Cubes

• Transformation of linear expressions and expressions reduced to them.Linear expressions. Properties of powers

• Transformation of linear expressions and expressions reduced to them.Expressions reduced to linear expressions

• Transformation of linear expressions and expressions reduced to them.Fractional expressions. Properties of fractions. Rational coefficients

• Transformation of linear expressions and expressions reduced to them.Fractional expressions. Properties of fractions. Integer coefficients

• Transformation of linear expressions and expressions reduced to them.Fractional expressions. Method of substitution. Integer coefficients

• Transformation of linear expressions and expressions reduced to them.Fractional expressions. Method of substitution. Rational coefficients

• Transformation of linear expressions and expressions reduced to them.Linear expressions. Factorization of quadratic trinomial

• Transformation of linear expressions and expressions reduced to them.Linear expressions. Method of substitution. Distributive law

• Transformation of linear expressions and expressions reduced to them.Linear expressions. Method of substitution. Formulas of short multiplication

• Transformation of linear expressions and expressions reduced to them.Linear expressions. Method of substitution. Properties of powers

• Transformation of linear expressions and expressions reduced to them.Linear expressions. Method of substitution. Factorization of quadratic trinomial

• Transformation of linear expressions and expressions reduced to them.Linear expressions. Properties of fractions. Distributive law

• Transformation of linear expressions and expressions reduced to them.Linear expressions. Properties of fractions. Formulas of short multiplication

• Transformation of linear expressions and expressions reduced to them.Linear expressions. Properties of fractions. Properties of powers

• Transformation of linear expressions and expressions reduced to them.Linear expressions. Properties of fractions. Factorization of quadratic trinomial

• Transformation of quadratic algebraic expressions and expressions reduced to them.Elementary quadratic expressions

• Transformation of quadratic algebraic expressions and expressions reduced to them.Quadratic expressions containing fractions

• Transformation of quadratic algebraic expressions and expressions reduced to them.Quadratic expressions. Distributive law. Integer coefficients

• Transformation of quadratic algebraic expressions and expressions reduced to them.Quadratic expressions. Formulas of short multiplication

• Transformation of quadratic algebraic expressions and expressions reduced to them.Quadratic expressions. Distributive law. Rational coefficients

• Transformation of quadratic algebraic expressions and expressions reduced to them.Quadratic expressions. Decomposition of quadratic trinomial

• Transformation of quadratic algebraic expressions and expressions reduced to them.Quadratic expressions. Properties of powers

• Transformation of quadratic algebraic expressions and expressions reduced to them.Fractional algebraic expression

• Transformation of quadratic algebraic expressions and expressions reduced to them.Quadratic expressions. Grouping method

• Transformation of quadratic algebraic expressions and expressions reduced to them.Quadratic expressions. Method of substitution. Distributive law. Integer coefficients

• Transformation of quadratic algebraic expressions and expressions reduced to them.Quadratic expressions. Method of substitution. Distributive law. Rational coefficients

• Transformation of quadratic algebraic expressions and expressions reduced to them.Quadratic expressions. Method of substitution. Formulas of short multiplication. Integer coefficients

• Transformation of quadratic algebraic expressions and expressions reduced to them.Quadratic expressions. Method of substitution. Formulas of short multiplication. Rational coefficients

• Transformation of quadratic algebraic expressions and expressions reduced to them.Quadratic expressions. Method of substitution. Grouping method

• Transformation of quadratic algebraic expressions and expressions reduced to them.Quadratic expressions. Method of substitution. Factorization of quadratic trinomial

• Transformation of quadratic algebraic expressions and expressions reduced to them.Fractional expressions. Method of substitution. Distributive law. Integer coefficients

• Transformation of quadratic algebraic expressions and expressions reduced to them.Fractional expressions. Method of substitution. Distributive law. Rational coefficients

• Transformation of quadratic algebraic expressions and expressions reduced to them.Fractional expressions. Method of substitution. Formulas of short multiplication. Integer coefficients

• Transformation of quadratic algebraic expressions and expressions reduced to them.Fractional expressions. Method of substitution. Formulas of short multiplication. Rational coefficients

• Transformation of algebraic high-degree expressions.High degrees. Bezout theorem. Standard problems. Integer roots

• Transformation of algebraic high-degree expressions.High degrees. Bezout theorem. Irrational roots

• Transformation of algebraic high-degree expressions.High degrees. Bezout theorem. Reducible problems. Integer roots

• Transformation of algebraic high-degree expressions.High degrees. Bezout theorem. Reducible problems

• Transformation of algebraic high-degree expressions.High degrees. Grouping method

• Transformation of algebraic high-degree expressions.High degrees. Perfect square

• Transformation of algebraic high-degree expressions.High degrees. Bezout theorem. Reducible problems. Irrational roots

• Transformation of algebraic high-degree expressions.High degrees. Distributive law

• Transformation of algebraic high-degree expressions.High degrees. Grouping method

• Transformation of algebraic high-degree expressions.High degrees. Formulas of short multiplication

• Transformation of algebraic high-degree expressions.High degrees. Difference of squares

• Transformation of algebraic high-degree expressions.High degrees. Perfect square

• Transformation of algebraic high-degree expressions.High degrees. Perfect cube

• Transformation of algebraic high-degree expressions.High degrees. Factorization of quadratic trinomial

• Transformation of algebraic high-degree expressions.High degrees. Properties of fractions

• Transformation of algebraic high-degree expressions.High degrees. Properties of powers

• Transformation of algebraic high-degree expressions.High degrees. Difference and sum of cubes

• Transformation of algebraic high-degree expressions.High degrees. Method of substitution

• Transformation of fractional algebraic expressions.Elementary fractional algebraic expressions

• Transformation of fractional algebraic expressions.Fractional algebraic expressions reduced to a fraction with linear expression in numerator

• Transformation of fractional algebraic expressions.Fractional algebraic expressions reduced to a fraction with quadratic expression in numerator

• Transformation of fractional algebraic expressions.Fractional algebraic expressions reduced to a fraction with cubic expression in numerator

• Transformation of fractional algebraic expressions.Fractional algebraic expressions reduced to a fraction with biquadratic expression in numerator

• Transformation of fractional algebraic expressions.Fractional algebraic expressions reduced to a fraction with reciprocal expression in numerator

• Transformation of fractional algebraic expressions.Fractional algebraic expressions reduced to a fraction with reciprocal expression in numerator. Method of substitution

• Factorization of linear expressions and expressions reduced to them.Elementary linear expressions

• Factorization of linear expressions and expressions reduced to them.Elementary linear expressions containing fractions

• Factorization of linear expressions and expressions reduced to them.Linear expressions. Distributive law

• Factorization of linear expressions and expressions reduced to them.Linear expressions. Formulas of short multiplication

• Factorization of linear expressions and expressions reduced to them.Linear expressions. Formulas of short multiplication. Cubes

• Factorization of linear expressions and expressions reduced to them.Linear expressions. Properties of fractions

• Factorization of linear expressions and expressions reduced to them.Linear expressions. Properties of powers

• Factorization of linear expressions and expressions reduced to them.Expressions reduced to linear expressions

• Factorization of linear expressions and expressions reduced to them.Fractional expressions reduced to linear expressions

• Factorization of linear expressions and expressions reduced to them.Fractional expressions. Properties of fractions. Rational coefficients

• Factorization of linear expressions and expressions reduced to them.Fractional expressions. Properties of fractions. Integer coefficients

• Factorization of linear expressions and expressions reduced to them.Fractional expressions. Method of substitution. Integer coefficients

• Factorization of linear expressions and expressions reduced to them.Fractional expressions. Method of substitution. Rational coefficients

• Factorization of linear expressions and expressions reduced to them.Linear expressions containing modulus

• Factorization of linear expressions and expressions reduced to them.Linear expressions. Factorization of quadratic trinomial

• Factorization of linear expressions and expressions reduced to them.Linear expressions. Method of substitution. Distributive law

• Factorization of linear expressions and expressions reduced to them.Linear expressions. Method of substitution. Formulas of short multiplication

• Factorization of linear expressions and expressions reduced to them.Linear expressions. Method of substitution. Properties of powers

• Factorization of linear expressions and expressions reduced to them.Linear expressions. Method of substitution. Factorization of quadratic trinomial

• Factorization of linear expressions and expressions reduced to them.Linear expressions. Properties of fractions. Distributive law

• Factorization of linear expressions and expressions reduced to them.Linear expressions. Properties of fractions. Formulas of short multiplication

• Factorization of linear expressions and expressions reduced to them.Linear expressions. Properties of fractions. Properties of powers

• Factorization of linear expressions and expressions reduced to them.Linear expressions. Properties of fractions. Factorization of quadratic trinomial

• Factorization of quadratic expressions and expressions reduced to them.Elementary quadratic expressions

• Factorization of quadratic expressions and expressions reduced to them.Quadratic expressions containing fractions

• Factorization of quadratic expressions and expressions reduced to them.Quadratic expressions. Distributive law. Integer coefficients

• Factorization of quadratic expressions and expressions reduced to them.Quadratic expressions. Formulas of short multiplication

• Factorization of quadratic expressions and expressions reduced to them.Quadratic expressions. Distributive law. Rational coefficients

• Factorization of quadratic expressions and expressions reduced to them.Quadratic expressions. Factorization of quadratic trinomial

• Factorization of quadratic expressions and expressions reduced to them.Quadratic expressions. Properties of powers

• Factorization of quadratic expressions and expressions reduced to them.Fractional algebraic expression

• Factorization of quadratic expressions and expressions reduced to them.Quadratic expressions containing modulus. Squaring method

• Factorization of quadratic expressions and expressions reduced to them.Quadratic expressions containing modulus. Separation of intervals

• Factorization of quadratic expressions and expressions reduced to them.Quadratic expressions. Grouping method

• Factorization of quadratic expressions and expressions reduced to them.Quadratic expressions. Method of substitution. Distributive law. Integer coefficients

• Factorization of quadratic expressions and expressions reduced to them.Quadratic expressions. Method of substitution. Distributive law. Rational coefficients

• Factorization of quadratic expressions and expressions reduced to them.Quadratic expressions. Method of substitution. Formulas of short multiplication. Integer coefficients

• Factorization of quadratic expressions and expressions reduced to them.Quadratic expressions. Method of substitution. Formulas of short multiplication. Rational coefficients

• Factorization of quadratic expressions and expressions reduced to them.Quadratic expressions. Method of substitution. Grouping method

• Factorization of quadratic expressions and expressions reduced to them.Quadratic expressions. Method of substitution. Factorization of quadratic trinomial

• Factorization of quadratic expressions and expressions reduced to them.Quadratic expressions. Method of substitution. Properties of powers

• Factorization of quadratic expressions and expressions reduced to them.Fractional expressions. Method of substitution. Distributive law. Integer coefficients

• Factorization of quadratic expressions and expressions reduced to them.Fractional expressions. Method of substitution. Distributive law. Rational coefficients

• Factorization of quadratic expressions and expressions reduced to them.Fractional expressions. Method of substitution. Formulas of short multiplication. Integer coefficients

• Factorization of quadratic expressions and expressions reduced to them.Fractional expressions. Method of substitution. Formulas of short multiplication. Rational coefficients

• Factorization of quadratic expressions and expressions reduced to them.Fractional expressions. Method of substitution. Factorization of quadratic trinomial

• Factorization of quadratic expressions and expressions reduced to them.Fractional expressions. Method of substitution. Properties of powers

• Factorization of quadratic expressions and expressions reduced to them.Fractional expressions. Method of substitution. Grouping method

• Factorization of quadratic expressions and expressions reduced to them.Quadratic expressions containing modulus. Method of substitution

• Factorization of algebraic high-degree expressions.High degrees. Bezout theorem. Standard problems. Integer roots

• Factorization of algebraic high-degree expressions.High degrees. Bezout theorem. Irrational roots

• Factorization of algebraic high-degree expressions.High degrees. Bezout theorem. Reducible problems. Integer roots

• Factorization of algebraic high-degree expressions.High degrees. Bezout theorem. Reducible problems

• Factorization of algebraic high-degree expressions.High degrees. Grouping method

• Factorization of algebraic high-degree expressions.High degrees. Perfect square

• Factorization of algebraic high-degree expressions.High degrees. Bezout theorem. Reducible problems. Irrational roots

• Factorization of algebraic high-degree expressions.High degrees. Distributive law

• Factorization of algebraic high-degree expressions.High degrees. Grouping method

• Factorization of algebraic high-degree expressions.High degrees. Formulas of short multiplication

• Factorization of algebraic high-degree expressions.High degrees. Difference of squares

• Factorization of algebraic high-degree expressions.High degrees. Perfect square

• Factorization of algebraic high-degree expressions.High degrees. Perfect cube

• Factorization of algebraic high-degree expressions.High degrees. Factorization of quadratic trinomial

• Factorization of algebraic high-degree expressions.High degrees. Properties of fractions

• Factorization of algebraic high-degree expressions.High degrees. Properties of powers

• Factorization of algebraic high-degree expressions.High degrees. Difference and sum of cubes

• Factorization of algebraic high-degree expressions.High degrees. Method of substitution

• Factorization of fractional algebraic expressions.Elementary fractional algebraic expressions

• Factorization of fractional algebraic expressions.Fractional algebraic expressions reduced to a fraction with linear expression in numerator

• Factorization of fractional algebraic expressions.Fractional algebraic expressions reduced to a fraction with quadratic expression in numerator

• Factorization of fractional algebraic expressions.Fractional algebraic expressions reduced to a fraction with cubic expression in numerator

• Factorization of fractional algebraic expressions.Fractional algebraic expressions reduced to a fraction with biquadratic expression in numerator

• Factorization of fractional algebraic expressions.Fractional algebraic expressions reduced to a fraction with reciprocal expression in numerator

• Factorization of fractional algebraic expressions.Fractional algebraic expressions reduced to a fraction with reciprocal expression in numerator. Method of substitution

• Proof of identity. Linear expressions and expressions reduced to them.Elementary linear expressions

• Proof of identity. Linear expressions and expressions reduced to them.Elementary linear expressions containing fractions

• Proof of identity. Linear expressions and expressions reduced to them.Linear expressions. Distributive law

• Proof of identity. Linear expressions and expressions reduced to them.Linear expressions. Formulas of short multiplication

• Proof of identity. Linear expressions and expressions reduced to them.Linear expressions. Formulas of short multiplication. Cubes

• Proof of identity. Linear expressions and expressions reduced to them.Linear expressions. Properties of fractions

• Proof of identity. Linear expressions and expressions reduced to them.Linear expressions. Properties of powers

• Proof of identity. Linear expressions and expressions reduced to them.Expressions reduced to linear expressions

• Proof of identity. Linear expressions and expressions reduced to them.Fractional expressions reduced to linear expressions

• Proof of identity. Linear expressions and expressions reduced to them.Fractional expressions. Properties of fractions. Rational coefficients

• Proof of identity. Linear expressions and expressions reduced to them.Fractional expressions. Properties of fractions. Integer coefficients

• Proof of identity. Linear expressions and expressions reduced to them.Fractional expressions. Method of substitution. Integer coefficients

• Proof of identity. Linear expressions and expressions reduced to them.Fractional expressions. Method of substitution. Rational coefficients

• Proof of identity. Linear expressions and expressions reduced to them.Linear expressions containing modulus

• Proof of identity. Linear expressions and expressions reduced to them.Linear expressions. Factorization of quadratic trinomial

• Proof of identity. Linear expressions and expressions reduced to them.Linear expressions. Method of substitution. Distributive law

• Proof of identity. Linear expressions and expressions reduced to them.Linear expressions. Method of substitution. Formulas of short multiplication

• Proof of identity. Linear expressions and expressions reduced to them.Linear expressions. Method of substitution. Properties of powers

• Proof of identity. Linear expressions and expressions reduced to them.Linear expressions. Method of substitution. Factorization of quadratic trinomial

• Proof of identity. Linear expressions and expressions reduced to them.Linear expressions. Properties of fractions. Distributive law

• Proof of identity. Linear expressions and expressions reduced to them.Linear expressions. Properties of fractions. Formulas of short multiplication

• Proof of identity. Linear expressions and expressions reduced to them.Linear expressions. Properties of fractions. Properties of powers

• Proof of identity. Linear expressions and expressions reduced to them.Linear expressions. Properties of fractions. Factorization of quadratic trinomial

• Proof of identity. Quadratic expressions and expressions reduced to them.Elementary quadratic expressions

• Proof of identity. Quadratic expressions and expressions reduced to them.Quadratic expressions containing fractions

• Proof of identity. Quadratic expressions and expressions reduced to them.Quadratic expressions. Distributive law. Integer coefficients

• Proof of identity. Quadratic expressions and expressions reduced to them.Quadratic expressions. Formulas of short multiplication

• Proof of identity. Quadratic expressions and expressions reduced to them.Quadratic expressions. Distributive law. Rational coefficients

• Proof of identity. Quadratic expressions and expressions reduced to them.Quadratic expressions. Factorization of quadratic trinomial

• Proof of identity. Quadratic expressions and expressions reduced to them.Quadratic expressions. Properties of powers

• Proof of identity. Quadratic expressions and expressions reduced to them.Fractional algebraic expression

• Proof of identity. Quadratic expressions and expressions reduced to them.Quadratic expressions containing modulus. Squaring method

• Proof of identity. Quadratic expressions and expressions reduced to them.Quadratic expressions containing modulus. Separation of intervals

• Proof of identity. Quadratic expressions and expressions reduced to them.Quadratic expressions. Grouping method

• Proof of identity. Quadratic expressions and expressions reduced to them.Quadratic expressions. Method of substitution. Distributive law. Integer coefficients

• Proof of identity. Quadratic expressions and expressions reduced to them.Quadratic expressions. Method of substitution. Distributive law. Rational coefficients

• Proof of identity. Quadratic expressions and expressions reduced to them.Quadratic expressions. Method of substitution. Formulas of short multiplication. Integer coefficients

• Proof of identity. Quadratic expressions and expressions reduced to them.Quadratic expressions. Method of substitution. Formulas of short multiplication. Rational coefficients

• Proof of identity. Quadratic expressions and expressions reduced to them.Quadratic expressions. Method of substitution. Grouping method

• Proof of identity. Quadratic expressions and expressions reduced to them.Quadratic expressions. Method of substitution. Factorization of quadratic trinomial

• Proof of identity. Quadratic expressions and expressions reduced to them.Quadratic expressions. Method of substitution. Properties of powers

• Proof of identity. Quadratic expressions and expressions reduced to them.Fractional expressions. Method of substitution. Distributive law. Integer coefficients

• Proof of identity. Quadratic expressions and expressions reduced to them.Fractional expressions. Method of substitution. Distributive law. Rational coefficients

• Proof of identity. Quadratic expressions and expressions reduced to them.Fractional expressions. Method of substitution. Formulas of short multiplication. Integer coefficients

• Proof of identity. Quadratic expressions and expressions reduced to them.Fractional expressions. Method of substitution. Formulas of short multiplication. Rational coefficients

• Proof of identity. Quadratic expressions and expressions reduced to them.Fractional expressions. Method of substitution. Factorization of quadratic trinomial

• Proof of identity. Quadratic expressions and expressions reduced to them.Fractional expressions. Method of substitution. Properties of powers

• Proof of identity. Quadratic expressions and expressions reduced to them.Fractional expressions. Method of substitution. Grouping method

• Proof of identity. Quadratic expressions and expressions reduced to them.Quadratic expressions containing modulus. Method of substitution

• Proof of identity. High-degree expressions.High degrees. Bezout theorem. Standard problems. Integer roots

• Proof of identity. High-degree expressions.High degrees. Bezout theorem. Irrational roots

• Proof of identity. High-degree expressions.High degrees. Bezout theorem. Reducible problems. Integer roots

• Proof of identity. High-degree expressions.High degrees. Bezout theorem. Reducible problems

• Proof of identity. High-degree expressions.High degrees. Grouping method

• Proof of identity. High-degree expressions.High degrees. Perfect square

• Proof of identity. High-degree expressions.High degrees. Bezout theorem. Reducible problems. Irrational roots

• Proof of identity. High-degree expressions.High degrees. Distributive law

• Proof of identity. High-degree expressions.High degrees. Grouping method

• Proof of identity. High-degree expressions.High degrees. Formulas of short multiplication

• Proof of identity. High-degree expressions.High degrees. Difference of squares

• Proof of identity. High-degree expressions.High degrees. Perfect square

• Proof of identity. High-degree expressions.High degrees. Perfect cube

• Proof of identity. High-degree expressions.High degrees. Factorization of quadratic trinomial

• Proof of identity. High-degree expressions.High degrees. Properties of fractions

• Proof of identity. High-degree expressions.High degrees. Properties of powers

• Proof of identity. High-degree expressions.High degrees. Difference and sum of cubes

• Proof of identity. High-degree expressions.High degrees. Method of substitution

• Proof of identity. Fractional algebraic expressions.Elementary fractional algebraic expressions

• Proof of identity. Fractional algebraic expressions.Fractional algebraic expressions reduced to a fraction with linear expression in numerator

• Proof of identity. Fractional algebraic expressions.Fractional algebraic expressions reduced to a fraction with quadratic expression in numerator

• Proof of identity. Fractional algebraic expressions.Fractional algebraic expressions reduced to a fraction with cubic expression in numerator

• Proof of identity. Fractional algebraic expressions.Fractional algebraic expressions reduced to a fraction with biquadratic expression in numerator

• Proof of identity. Fractional algebraic expressions.Fractional algebraic expressions reduced to a fraction with reciprocal expression in numerator

• Proof of identity. Fractional algebraic expressions.Fractional algebraic expressions reduced to a fraction with reciprocal expression in numerator. Method of substitution