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

May 20, 2017

There is no solution.

Explanation:

First rearrange the equation so that a LCM of the denominator can be obtained.
${x}^{2} / \left({x}^{2} - 4\right) = \frac{x}{x + 2} - \frac{2}{2 - x}$
${x}^{2} / \left({x}^{2} - 4\right) = \frac{x}{x + 2} - \frac{2}{- 1 \cdot \left(x - 2\right)}$
${x}^{2} / \left({x}^{2} - 4\right) = \frac{x}{x + 2} + \frac{2}{x - 2}$
Now, multiply both sides by $\left(x - 2\right) \left(x + 2\right)$, since this is the LCM.
Doing this gets:
${x}^{2} = x \left(x - 2\right) + 2 \left(x + 2\right)$
${x}^{2} = {x}^{2} - 2 x + 2 x + 4$
$0 = 4$ which is not possible.
There is no solution.