Answer
$-\frac{(2a+3b)(a+2b)}{(b+5a)(2a-3b)}$.
Work Step by Step
The given expression is
$=\frac{2a^2-ab-6b^2}{2b^2+9ab-5a^2}\div \frac{2a^2-7ab+6b^2}{a^2-4b^2}$
Factor.
$=\frac{(2a+3b)(a-2b)}{(b+5a)(2b-a)}\div \frac{(a-2b)(2a-3b)}{(a-2b)(a+2b)}$
$=\frac{(2a+3b)(a-2b)}{(b+5a)(2b-a)}\times \frac{(a-2b)(a+2b)}{(a-2b)(2a-3b)}$
Divide out the common terms.
$=-\frac{(2a+3b)(a+2b)}{(b+5a)(2a-3b)}$.
