# How do you solve x/(x+4) - 4/(x-4) = (x^2+16)/(x^2-16)?

Jun 16, 2015

NO SOLUTIONS!!!!

#### Explanation:

Consider as common denominator ${x}^{2} - 16 = \left(x - 4\right) \left(x + 4\right)$:
$\frac{x \left(x - 4\right) - 4 \left(x + 4\right)}{\cancel{\left({x}^{2} - 16\right)}} = \frac{{x}^{2} + 16}{\cancel{\left({x}^{2} - 16\right)}}$
$\cancel{{x}^{2}} - 4 x - 4 x - 16 = \cancel{{x}^{2}} + 16$
$- 8 x = 32$
$x = - 4$
BUT this value cannot be accpeted because it makes the denominator of my original expression equal to ZERO!!!
So...NO real solutions!!!!