# How do you simplify (8x+16) / (x^2-1 )*( x+1)/(4x+8)?

Sep 21, 2015

The answer is $\frac{2}{x - 1}$.

#### Explanation:

$\frac{8 x + 16}{{x}^{2} - 1} \cdot \frac{x + 1}{4 x + 8}$

Factor out $2$ from $\left(8 x + 16\right)$.

$\frac{2 \left(4 x + 8\right)}{{x}^{2} - 1} \cdot \frac{x + 1}{4 x + 8}$

Cancel $\left(4 x + 8\right)$ in the numerator and denominator.

$\frac{2 \cancel{4 x + 8}}{{x}^{2} - 1} \cdot \frac{x + 1}{\cancel{4 x + 8}} =$

$\frac{2}{{x}^{2} - 1} \cdot \frac{x + 1}{1}$

Factor ${x}^{2} - 1$.

$\frac{2}{\left(x + 1\right) \left(x - 1\right)} \cdot \frac{x + 1}{1}$

Cancel $x + 1$ in the numerator and denominator.

$\frac{2}{\cancel{x + 1} \left(x - 1\right)} \cdot \frac{\cancel{x + 1}}{1} =$

$\frac{2}{x - 1}$