# How do you write 4/(x+2)+3/(x-2) as a single fraction in its simplest form?

Jan 9, 2017

The answer is $= \frac{7 x - 2}{{x}^{2} - 4}$

#### Explanation:

$\left(a + b\right) \left(a - b\right) = {a}^{2} - {b}^{2}$

The common denominator is $= \left(x + 2\right) \left(x - 2\right)$

$\frac{4}{x + 2} + \frac{3}{x - 2}$

$= \frac{4 \left(x - 2\right) + 3 \left(x + 2\right)}{\left(x + 2\right) \left(x - 2\right)}$

$= \frac{4 x - 8 + 3 x + 6}{{x}^{2} - 4}$

$= \frac{7 x - 2}{{x}^{2} - 4}$