Partial fractions

Math

Definition

A technique for breaking a complex rational expression into a sum of simpler fractions, making integration or inverse Laplace transforms possible. Each factor in the denominator gets its own fraction.

How It Works

  1. Factor the denominator completely
  2. Write one fraction for each factor with unknown numerator constants
  3. Multiply both sides by the common denominator
  4. Solve for the unknown constants by substituting strategic values or comparing coefficients
  5. Write the final decomposition

Examples

  • (2x+1)/((x+1)(x-1)) = A/(x+1) + B/(x-1)
  • Breaking 1/(x²-1) into 1/2·(1/(x-1) - 1/(x+1))
  • Used to integrate rational functions in calculus

Related Terms

Polynomial division Simplifying rational expressions Antiderivatives

Study This Concept

Practice partial fractions with free review games in these units:

Pre-Calculus Unit 2: Polynomial and Rational Functions