Simplifying rational expressions

Math

Definition

The process of reducing a fraction that contains polynomials in the numerator and denominator by factoring both and canceling common factors. The result is the simplest equivalent expression, valid for all values where the original denominator is not zero.

How It Works

  1. Factor the numerator completely.
  2. Factor the denominator completely.
  3. Identify and cancel any common factors.
  4. State any restrictions on the variable (values that make the original denominator zero).

Examples

  • (x² − 9)/(x + 3) simplifies to (x − 3) since x² − 9 = (x+3)(x−3)
  • (2x² + 4x)/(2x) simplifies to x + 2

Related Terms

Factoring trinomials Difference of squares Solving rational equations Fraction operations

Study This Concept

Practice simplifying rational expressions with free review games in these units:

Algebra 2 Unit 5: Rational Functions