# How do you write the partial fraction decomposition of the rational expression (x - 16) / (x^2 + x - 2)?

Dec 13, 2015

$\frac{6}{x + 2} - \frac{5}{x - 1}$

#### Explanation:

The expression equals $\frac{x - 16}{\left(x + 2\right) \left(x - 1\right)}$.

$\frac{x - 16}{\left(x + 2\right) \left(x - 1\right)} = \frac{A}{x + 2} + \frac{B}{x - 1}$

$x - 16 = A \left(x - 1\right) + B \left(x + 2\right)$

IF $x = 1$:

$- 15 = 3 B$
$B = - 5$

IF $x = - 2$:

$- 18 = - 3 A$
$A = 6$

$\frac{x - 16}{{x}^{2} + x - 2} = \frac{6}{x + 2} - \frac{5}{x - 1}$