How do you simplify ((x^2-2x-4)/(x^2+2x-8))*((3x^2+15x)/(x+1))/((4x^2-100)/(x^2-x-20))?

$\setminus \frac{3 x \left({x}^{2} - 2 x - 4\right)}{4 \left(x + 1\right) \left(x - 2\right)}$

Explanation:

Given that

$\left(\setminus \frac{{x}^{2} - 2 x - 4}{{x}^{2} + 2 x - 8}\right) \setminus \cdot \setminus \frac{\setminus \frac{3 {x}^{2} + 15 x}{x + 1}}{\setminus \frac{4 {x}^{2} - 100}{{x}^{2} - x - 20}}$

$= \left(\setminus \frac{{x}^{2} - 2 x - 4}{\left(x + 4\right) \left(x - 2\right)}\right) \setminus \cdot \setminus \frac{\setminus \frac{3 x \left(x + 5\right)}{x + 1}}{\setminus \frac{4 \left(x + 5\right) \left(x - 5\right)}{\left(x - 5\right) \left(x + 4\right)}}$

$= \setminus \frac{\left({x}^{2} - 2 x - 4\right)}{\left(x + 4\right) \left(x - 2\right)} \left(\setminus \frac{3 x \left(x + 4\right)}{4 \left(x + 1\right)}\right)$

$= \setminus \frac{\left({x}^{2} - 2 x - 4\right)}{\left(x - 2\right)} \setminus \cdot \setminus \frac{3 x}{4 \left(x + 1\right)}$

$= \setminus \frac{3 x \left({x}^{2} - 2 x - 4\right)}{4 \left(x + 1\right) \left(x - 2\right)}$