1. Copyright © Cengage Learning. All rights reserved.
7.4
PARTIAL FRACTIONS
Copyright © Cengage Learning. All rights reserved.

2. What You Should Learn
Recognize partial fraction decompositions of rational expressions.
Find partial fraction decompositions of rational expressions.

3. Introduction
We will learn to write a rational expression as the sum of two or more simpler rational expressions. For example, the rational expression
can be written as the sum of two fractions with first-degree denominators. That is,

4. Introduction
Each fraction on the right side of the equation is a partial
fraction, and together they make up the partial fraction
decomposition of the left side.

5. Introduction

6. Partial Fraction Decomposition
Algebraic techniques for determining the constants in the
numerators of partial fractions are demonstrated in the
examples that follow.
Note that the techniques vary slightly, depending on the type of factors of the denominator: linear or quadratic, distinct or repeated.

7. Example 1 – Distinct Linear Factors
Write the partial fraction decomposition of

8. Partial Fraction Decomposition

9. Example 2
Write the partial fraction decomposition of

10. Example 3
Write the partial fraction decomposition of

11. Example 4
Write the partial fraction decomposition of

12. Partial Fraction Decomposition
Keep in mind that for improper rational expressions such as
you must first divide before applying partial fraction decomposition.

13. Example 6
Write the partial fraction decomposition of