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.

First, you should notice the difference of squares formula (twice) in the denominator.  $(x-2)(x+2)=x^2-4$  Then $(x^2-4)(x^2+4)=x^4-16$ so we have $\frac {x^5}{x^4-16}=x+\frac {16x}{x^4-16}$  The rest is a partial fraction decomposition of the second term.
