# How do you solve 2/(x +6) = 9/8 - 4/(x+6)?

Jan 2, 2016

$x = - \frac{2}{3}$

#### Explanation:

Original solution
Place on a common denominator and solve the resulting linear equation.
$\frac{16}{8 x + 48}$ = $\frac{9 x + 54}{8 x + 48}$ - $\frac{32}{8 x + 48}$

16 - 54 + 32 = 9x

-6 = 9x

$- \frac{2}{3}$ = x

Simplier solution
$\frac{2}{x + 6} = \frac{9}{8} - \frac{4}{x + 6}$
$\frac{2}{x + 6} + \frac{4}{x + 6} = \frac{9}{8}$
$\frac{6}{x + 6} = \frac{9}{8}$
Multiply both sides by $\left(x + 6\right)$ and divide by $\frac{9}{8}$
$6 \cdot \frac{8}{9} = x + 6$
$x = \frac{2 \cdot 8}{3} - 6 = \frac{16}{3} - 6 = 5 \frac{1}{3} - 6 = - \frac{2}{3}$
The solution is $- \frac{2}{3}$.