Answer
$\frac{1}{(2x-5)(3x-2)}$
Work Step by Step
We switch from division to multiplication by taking the reciprocal of the right fraction. Then we factor and simplify:
$\displaystyle \frac{2x+1}{2x^{2}+x-15}\div\frac{6x^{2}-x-2}{x+3}=\frac{2x+1}{(x+3)(2x-5)}*\frac{x+3}{(2x+1)(3x-2)}=\frac{1}{(2x-5)(3x-2)}$
