Answer
$\frac{A}{x} + \frac{B}{x^{2}} + \frac{C}{(x-4)} + \frac{D}{(x-4)^{2}}$
Work Step by Step
For each power of x and for each power of (x- 4), we need a partial fraction:
$\frac{A}{x} + \frac{B}{x^{2}} + \frac{C}{(x-4)} + \frac{D}{(x-4)^{2}}$