# How do you write the partial fraction decomposition of the rational expression 8 / [ ( x + 2 ) ( x^2 + 4 ) ]?

May 21, 2016

$\frac{1}{x + 2} + \frac{2 - x}{{x}^{2} + 4}$

#### Explanation:

Solve these three equations,

From 4A+2C=8 , A= $\left(2 - \frac{C}{2}\right)$

From 2B+C=0, B= $- \frac{C}{2}$

Therefore, A+B=2-C=0, hence C=2, B=-1 and A= 1.

The partial fractions are therefore $\frac{1}{x + 2} + \frac{2 - x}{{x}^{2} + 4}$