# How do you write the partial fraction decomposition of the rational expression  2 / (x(4x-1))?

Dec 29, 2015

$\frac{2}{x \left(4 x - 1\right)} = \frac{8}{4 x - 1} - \frac{2}{x}$

#### Explanation:

Split into parts.

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

Multiply for a common denominator of $x \left(4 x - 1\right)$.

$2 = A \left(4 x - 1\right) + B x$

Plug in $\frac{1}{4}$ for $x$.

$2 = \frac{1}{4} B$

$B = 8$

Plug in $0$ for $x$.

$2 = - A$

$A = - 2$

Thus,

$\frac{2}{x \left(4 x - 1\right)} = \frac{8}{4 x - 1} - \frac{2}{x}$