# How do you simplify (x+6)/(x+7) - (x-7)/(x-6)?

Apr 23, 2016

$\frac{13}{{x}^{2} + x - 42}$

#### Explanation:

$\frac{x + 6}{x + 7} - \frac{x - 7}{x - 6}$

= $\frac{\left(x + 6\right) \left(x - 6\right) - \left(x - 7\right) \left(x + 7\right)}{\left(x + 7\right) \left(x - 6\right)}$

= $\frac{\left({x}^{2} - 36\right) - \left({x}^{2} - 49\right)}{{x}^{2} + 7 x - 6 x - 42}$

= $\frac{{x}^{2} - 36 - {x}^{2} + 49}{{x}^{2} + x - 42}$

= $\frac{13}{{x}^{2} + x - 42}$