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

Dec 14, 2015

$\frac{x + 2}{x \left(x - 4\right)} = \frac{3}{2 \left(x - 4\right)} - \frac{1}{2 x}$

#### Explanation:

$\frac{x + 2}{x \left(x - 4\right)} = \frac{A}{x} + \frac{B}{x - 4}$

$x + 2 = A \left(x - 4\right) + B x$

IF $x = 0$:

$2 = - 4 A$
$A = - \frac{1}{2}$

IF $x = 4$:

$6 = 4 B$
$B = \frac{3}{2}$

Therefore:

$\frac{x + 2}{x \left(x - 4\right)} = \frac{3}{2 \left(x - 4\right)} - \frac{1}{2 x}$