#### Answer

$\frac{(2x+5)(x-5)}{4}$

#### Work Step by Step

First, we have to multiply together the numerators and the denominators:
$\frac{2x+5}{4x-12}\cdot(x^2-8x+15) = \frac{2x+5}{4x-12}\cdot\frac{x^2-8x+15}{1} = \frac{(2x+5)(x^2-8x+15)}{4x-12}$
Next, we factor the polynomial and simplify:
$\frac{(2x+5)(x-5)(x-3)}{4(x-3)} = \frac{(2x+5)(x-5)}{4}$