Answer
$\frac{5a(2a+b)(3a-2b)}{b^2(a+2b)(a-b)}$
Work Step by Step
$\frac{2a+b}{b^2}*\frac{3a^2-2ab}{ab+2b^2}\div\frac{a^2-3ab+2b^2}{5ab-10b^2}$
$\frac{2a+b}{b^2}*\frac{a(3a-2b)}{b(a+2b)}\div\frac{(a-b)(a-2b)}{5b(a-2b)}$
$\frac{2a+b}{b^2}*\frac{a(3a-2b)}{b(a+2b)}\div\frac{(a-b)}{5b}$
$\frac{2a+b}{b^2}*\frac{a(3a-2b)}{b(a+2b)}*\frac{5b}{(a-b)}$
$\frac{2a+b}{b^2}*\frac{a(3a-2b)}{(a+2b)}*\frac{5}{(a-b)}$
$\frac{5a(2a+b)(3a-2b)}{b^2(a+2b)(a-b)}$
