# How do you solve \frac{x}{x^2-36}+\frac{1}{x-6}=\frac{1}{x+6}?

Nov 13, 2014

$\frac{x}{{x}^{2} - 36} + \frac{1}{x - 6} = \frac{1}{x + 6}$

by factoring out the denominator of the first term,

$\implies \frac{x}{\left(x - 6\right) \left(x + 6\right)} + \frac{1}{x - 6} = \frac{1}{x + 6}$

by multiplying by $\left(x - 6\right) \left(x + 6\right)$,

$\implies x + \left(x + 6\right) = \left(x - 6\right)$

by subtracting $x$,

$\implies x + 6 = - 6$

by subtracting $6$,

$\implies x = - 12$

I hope that this was helpful.