Step-by-Step Partial Fraction Decomposition

type 1

type 2

type 3

type 4

1. Check if the functionis a proper rational function.

2. Factor the denominator.

3. Name the type of partial fraction.

4. Write the partial fraction withvariables.

5. Multiply by the denominator,group like terms and set thatto the numerator.

6. Equate coefficients and solvethe resulting system of equations.

7. Substitute in the partial fractionform of the rational function.

2

x

+2x-1

2

3

x

+3

2

x

-2x

This Demonstration shows the step-by-step solution to a partial fraction decomposition, considering four types of denominator factorization.

The Wolfram Language function Apart does partial fraction decomposition in one step.

[1] J. Stewart, Essential Calculus: Early Transcendentals, Belmont, CA: Brooks/Cole, Cengage Learning, 2011.

Maria Camila Arguello Gomez