Answer
$\frac{4x}{(x+7)(2x+3)}$
Work Step by Step
The reciprocal of a fraction $\frac{x}{y}$ is $\frac{y}{x}$. Dividing by a fraction is the same thing as multiplying by that fraction's reciprocal.
First, we have to multiply together the numerators and the denominators:
$\frac{8x^2-12x}{x+7}\div(4x^2-9) = \frac{8x^2-12x}{x+7}\div\frac{4x^2-9}{1} = \frac{8x^2-12x}{x+7}\cdot\frac{1}{4x^2-9} = \frac{8x^2-12x}{(x+7)(4x^2-9)}$
Then, we simplify:
$\frac{(2x-3)(4x)}{(x+7)(2x-3)(2x+3)} = \frac{4x}{(x+7)(2x+3)}$
