Answer
$\frac{A}{x} + \frac{B}{x^{2}}+ \frac{C}{x^{3}} + \frac{Dx + E}{x^{2}+2} + \frac{Fx+G}{(x^{2}+2)^{2}}$
Work Step by Step
We must have a linear numerator for each power, and there must be a partial fraction for each power of $(x^{2} + 2)$ and x:
$\frac{A}{x} + \frac{B}{x^{2}}+ \frac{C}{x^{3}} + \frac{Dx + E}{x^{2}+2} + \frac{Fx+G}{(x^{2}+2)^{2}}$
