# How do you add and simplify \frac { 7} { x - 3} + \frac { 2} { x + 7}?

Jun 22, 2017

$\frac{9 x - 43}{{x}^{2} - 4 x - 24}$

#### Explanation:

To combine fractions, they need to have a "common denominator".

$\frac{x + 7}{x + 7} \times \frac{7}{x - 3} + \frac{2}{x + 7} \times \frac{x - 3}{x - 3}$

$\frac{7 x + 49}{{x}^{2} - 4 x - 24} + \frac{2 x - 6}{{x}^{2} - 4 x - 24}$

$\frac{7 x + 49 + 2 x - 6}{{x}^{2} - 4 x - 24}$

combine like-terms

$\frac{9 x - 43}{{x}^{2} - 4 x - 24}$