# How do you solve 2/(x+1)+x/(x-1)=2/(x^2-1)?

Sep 25, 2016

$x = - 4$

#### Explanation:

Note that ${x}^{2} - 1 = \left(x - 1\right) \left(x + 1\right)$

Multiply the given equation through by ${x}^{2} - 1 = \left(x - 1\right) \left(x + 1\right)$ to get:

$2 \left(x - 1\right) + x \left(x + 1\right) = 2$

Multiply out to get:

$2 x - 2 + {x}^{2} + x = 2$

Simplify to get:

${x}^{2} + 3 x - 2 = 2$

Subtract $2$ from both sides and transpose to get:

$0 = {x}^{2} + 3 x - 4 = \left(x + 4\right) \left(x - 1\right)$

From this we find $x = 1$ or $x = - 4$

Note that $x = 1$ is a solution of the derived equation, but is not a solution of the original equation since it causes two of the denominators to be $0$.

So the only valid solution is $x = - 4$