Answer
$\displaystyle \frac{(a+2)(a-2)^{2}}{a^{4}}$
Work Step by Step
Factor what we can:
$ a^{2}-4=\quad$ ... difference of squares$\quad=(a+2)(a-2)$
$a^{2}+a=a(a+1)$
$ a^{2}-a-2=\quad$ ... factors of -2 whose sum is -1 ... are -2 and 1
$=(a-2)(a+1)$
$\displaystyle \frac{a^{2}-4}{a^{2}+a}\cdot\frac{a^{2}-a-2}{a^{3}}=\frac{(a+2)(a-2)(a-2)(a+1)}{a^{4}(a+1)}$
... cancel (a+1),
$=\displaystyle \frac{(a+2)(a-2)^{2}}{a^{4}}$
