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

May 3, 2016

I found no solutions (the left side is NOT equal to the right one)

#### Explanation:

Let us write it as:
${x}^{2} / \left({x}^{2} - 4\right) = \frac{x}{x + 2} \textcolor{red}{+ \frac{2}{x - 2}}$
we can use as common denominator $\left({x}^{2} - 4\right)$ which is equal to $\left(x + 2\right) \left(x - 2\right)$ and write:
${x}^{2} / \cancel{\left({x}^{2} - 4\right)} = \frac{x \left(x - 2\right) + 2 \left(x + 2\right)}{\cancel{\left({x}^{2} - 4\right)}}$
giving:
$\cancel{{x}^{2}} = \cancel{{x}^{2}} \cancel{- 2 x} + \cancel{2 x} + 4$

so we get $4 = 0$ which is not true