# How do you solve  x^2/(x^2-4) = x/(x+2)-2/(2-x)?

Mar 24, 2018

There is no solution

#### Explanation:

${x}^{2} / \left({x}^{2} - 4\right) = \frac{x}{x + 2} - \frac{2}{2 - x}$
Becomes ${x}^{2} / \left({x}^{2} - 4\right) = \frac{x}{x + 2} + \frac{2}{x - 2}$

On the right side, multiply and divide first fraction with $x - 2$
On the right side, multiply and divide second fraction with $x + 2$
We get,

Becomes ${x}^{2} / \left({x}^{2} - 4\right) = \frac{x \left(x - 2\right)}{\left(x + 2\right) \left(x - 2\right)} + \frac{2 \left(x + 2\right)}{\left(x - 2\right) \left(x + 2\right)}$

Becomes ${x}^{2} / \left({x}^{2} - 4\right) = \frac{{x}^{2} - 2 x + 2 x + 4}{{x}^{2} - 4}$

Becomes ${x}^{2} / \left({x}^{2} - 4\right) = \frac{{x}^{2} + 4}{{x}^{2} - 4}$

Becomes ${x}^{2} = \left({x}^{2} + 4\right)$

There is no solution