# Question #31f48

Jan 22, 2017

The answer is $= \frac{3}{x - 1} ^ 2 + \frac{5}{x - 1}$

#### Explanation:

Let's do the partial fraction decomposition

$\frac{5 x - 2}{x - 1} ^ 2 = \frac{A}{x - 1} ^ 2 + \frac{B}{x - 1}$

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

The denomintors are the same, so we equalise the nunerators

$5 x - 2 = A + B \left(x - 1\right)$

Coefficients of x, $5 = B$

Let $x = 1$, $\implies$, $3 = A$

Therefore,

$\frac{5 x - 2}{x - 1} ^ 2 = \frac{3}{x - 1} ^ 2 + \frac{5}{x - 1}$