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

Mar 13, 2016

This identity will result in:
${x}^{2} / \left({x}^{2} - 4\right) = \frac{{x}^{2} + 4}{{x}^{2} - 4}$ so the solution does not exist...
Why?${x}^{2} / \left({x}^{2} - 4\right) \textcolor{red}{\ne} \frac{{x}^{2} + 4}{{x}^{2} - 4}$
Given: ${x}^{2} / \left({x}^{2} - 4\right) = \frac{x}{x + 2} - \frac{2}{2 - x}$
$R H S = \frac{x \left(2 - x\right) - \left(2 x + 4\right)}{- {x}^{2} + 4} = \frac{- {x}^{2} - 4}{- {x}^{2} + 4}$
$R H S = \frac{{x}^{2} + 4}{{x}^{2} - 4}$ clearly RHS is not equal to LHS so the solution to this one does not exist. So either you must made an error in writing down your question or you don't have a solution.