# How do you write the partial fraction decomposition of the rational expression 7/(x^2-14x)?

Dec 24, 2015

$\frac{7}{{x}^{2} - 14 x} = - \frac{1}{2 x} + \frac{1}{2 \left(x - 14\right)}$

#### Explanation:

Factor and then break up the denominator.

$\frac{7}{x \left(x - 14\right)} = \frac{A}{x} + \frac{B}{x - 14}$

Find a common denominator of $x \left(x - 14\right)$.

$7 = A \left(x - 14\right) + B x$

Plug in $0$ for $x$:

$7 = - 14 A$
$A = - \frac{1}{2}$

Plug in $14$ for $x$:

$7 = 14 B$
$B = \frac{1}{2}$

Plug these values into the original expression.

$\frac{7}{{x}^{2} - 14 x} = - \frac{1}{2 x} + \frac{1}{2 \left(x - 14\right)}$