Algebra and Trigonometry, 5th Edition

9.8 Partial Fractions

• Decompose rational expressions into partial fractions.

There are situations in calculus in which it is useful to write a rational expression as a sum of two or more simpler rational expressions. In the equation

$$\frac{4x-13}{{2x}^2+x-6}=\frac{3}{x+2}+\frac{-2}{2x-3},$$

for example, each fraction on the right side is called a partial fraction. The expression on the right side is the partial fraction decomposition of the rational expression on the left side. In this section, we learn how such decompositions are created.

Partial Fraction Decompositions

The procedure for finding the partial fraction decomposition of a rational expression involves factoring its denominator into linear factors and quadratic factors.

Procedure for Decomposing a Rational ...