Solving rational equations

Math

Definition

Finding the value of the variable in equations that contain fractions with polynomials. The main strategy is to multiply both sides by the least common denominator (LCD) to clear the fractions, then solve the resulting polynomial equation. Always check for extraneous solutions that make a denominator zero.

How It Works

  1. Identify the LCD of all fractions in the equation.
  2. Multiply every term by the LCD to clear all denominators.
  3. Solve the resulting equation.
  4. Check that solutions do not make any original denominator equal to zero.

Examples

  • 1/x + 1/3 = 1/2 → LCD is 6x → 6 + 2x = 3x → x = 6
  • x/(x−1) = 3/(x−1) + 2 → multiply by (x−1), then check x ≠ 1

Related Terms

Simplifying rational expressions Fraction operations Solving proportions

Study This Concept

Practice solving rational equations with free review games in these units:

Algebra 2 Unit 5: Rational Functions