# How do you simplify [(x^2-x)/(x+5)]*[(x^2+5x+4)/(x^4-x^2)]?

Jul 15, 2015

$\frac{x + 4}{x \left(x + 5\right)}$

#### Explanation:

Factor the terms:

$\left[\frac{{x}^{2} - x}{x + 5}\right] . \left[\frac{{x}^{2} + 5 x + 4}{{x}^{2} - {x}^{2}}\right] = \left[\frac{{x}^{2} - x}{x + 5}\right] . \left[\frac{\left(x + 1\right) \left(x + 4\right)}{x \left({x}^{2} - x\right) \left(x + 1\right)}\right]$

Cancel terms in numerator and denominator that are the same:

$\left[\frac{{x}^{2} - x}{x + 5}\right] . \left[\frac{\left(x + 1\right) \left(x + 4\right)}{x \left({x}^{2} - x\right) \left(x + 1\right)}\right] = \frac{x + 4}{x \left(x + 5\right)}$