Answer
$$\frac{x}{2\left(x+2\right)\left(x+1\right)}$$
Work Step by Step
Recall, one never divides by a fraction. Rather, if we want to divide by a fraction, we multiply by the reciprocal of the fraction. Recall, the reciprocal of a fraction is that fraction with the numerator and the denominator switched. Thus, we find:
$$ \frac{\left(x^2-x\right)}{4x^2+8x}\times \frac{2x}{\left(x^2-1\right)}\\ \frac{x\left(x-1\right)}{2\left(x+2\right)\left(x^2-1\right)}\\ \frac{x\left(x-1\right)}{2\left(x+2\right)\left(x+1\right)\left(x-1\right)}\\ \frac{x}{2\left(x+2\right)\left(x+1\right)}$$
