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

Feb 13, 2016

Place on the same denominator and solve.

#### Explanation:

the LCD (least common denominator) is ${x}^{2} - 4$

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

We can eliminate the denominators:

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

${x}^{2} = {x}^{2} - 2 x + 2 x + 4$

Everything eliminates themselves, so there is no solution.