How do I transform, with long division, this polynomial into the answer given? I need to transform:
$ \frac {x^5}{(x-2)(x+2)(x^2+4)}  $
into
$ \frac{-2x}{x^2+4} + x + \frac{1}{x-2} + \frac{1}{x+2} $
How can I solve it? 
Thanks.

Let me try. We have $$\frac{x^5}{(x-2)(x+2)(x^2+4)} = \frac{x^5}{x^4-16}= x + \frac{16x}{x^4-16} = x + 2x\left(\frac{1}{x^2-4} - \frac{1}{x^2+4}\right) = x -\frac{2x}{x^2+4} +\frac{2x}{(x+2)(x-2)} = x -\frac{2x}{x^2+4} + \frac{1}{x-2} + \frac{1}{x+2}.$$
