# How do you simplify and find the excluded value of (3) / (x+1) + (5) / ( x - 1) ?

Apr 12, 2016

First we say that $x \ne - 1 \mathmr{and} x \ne + 1$ or one of the denominators would be $= 0$ and that's not allowed.

#### Explanation:

Then we find a common denominator by multiplying:
$= \frac{3}{x + 1} \times \frac{x - 1}{x - 1} + \frac{5}{x - 1} \times \frac{x + 1}{x + 1}$

$= \frac{3 \left(x - 1\right)}{\left(x - 1\right) \left(x + 1\right)} + \frac{5 \left(x + 1\right)}{\left(x - 1\right) \left(x + 1\right)}$

$= \frac{3 x - 3 + 5 x + 5}{{x}^{2} - 1} = \frac{8 x + 2}{{x}^{2} - 1}$

And there is still the same restriction of $x \ne \pm 1$