# How do you simplify (x-1)/(x^2-1) +2/(5x+5)?

Jul 31, 2016

$\frac{x - 1}{{x}^{2} - 1} + \frac{2}{5 x + 5} = \frac{7}{5 x + 5}$

#### Explanation:

$\frac{x - 1}{{x}^{2} - 1} + \frac{2}{5 x + 5}$

= $\frac{x - 1}{\left(x - 1\right) \left(x + 1\right)} + \frac{2}{5 \left(x + 1\right)}$

= $\frac{1 \cancel{\left(x - 1\right)}}{\cancel{\left(x - 1\right)} \left(x + 1\right)} + \frac{2}{5 \left(x + 1\right)}$

= $\frac{1}{\left(x + 1\right)} + \frac{2}{5 \left(x + 1\right)}$

= $\frac{5 \times 1}{5 \left(x + 1\right)} + \frac{2}{5 \left(x + 1\right)}$

= $\frac{5}{5 \left(x + 1\right)} + \frac{2}{5 \left(x + 1\right)}$

= $\frac{7}{5 \left(x + 1\right)}$

= $\frac{7}{5 x + 5}$