Answer
$\frac{(a+4)(a-2)}{(a+2)(a^2)}$
Work Step by Step
$\frac{a^2+5a+4}{a^3}\div\frac{a^2+3a+2}{a^2-2a}$
$\frac{a^2+5a+4}{a^3}*\frac{a^2-2a}{a^2+3a+2}$
$\frac{(a+4)(a+1)}{a^3}*\frac{a(a-2)}{(a+2)(a+1)}$
$\frac{(a+4)(a+1)a(a-2)}{(a+2)(a+1)(a^3)}$
$\frac{(a+4)(a-2)}{(a+2)(a^2)}$
