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

Feb 16, 2016

You must make all the fractions equivalent by putting them on an equivalent denominator.

#### Explanation:

The LCD (Least Common Denominator) is (x + 2)(x - 2).

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

We can now eliminate the denominators.

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

${x}^{2} - {x}^{2} - 4 x - 8 = 0$

$- 4 x = 8$

$x = - 2$

Since x= -2 makes some of the denominators equal to 0, there is no solution to the equation.

Hooefully this helps!