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

Oct 4, 2015

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

#### Explanation:

$\frac{2}{x + 6} = \frac{9}{8} - \frac{4}{x + 6}$

$\frac{2}{x + 6} - \frac{9}{8} + \frac{4}{x + 6} = 0$

$\frac{2 \cdot 8 - 9 \left(x + 6\right) + 4 \cdot 8}{8 \left(x + 6\right)} = 0$

$\frac{16 - 9 x - 54 + 32}{8 \left(x + 6\right)} = 0$

$\frac{- 6 - 9 x}{8 \left(x + 6\right)} = 0$

$- 6 - 9 x = 0 \wedge x + 6 \ne 0$

$x = \frac{6}{-} 9 \wedge x \ne - 6$

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

Oct 4, 2015

x = -0.66666

#### Explanation:

2 / (x + 6) = 9 / 8 − 4 / (x + 6)
Transport − 4 / (x + 6) to the left hand side. We get
2 / (x + 6) + 4 / (x + 6) = 9 / 8
or 6 / (x + 6) = 9 / 8
Cross multiplying,
8 * 6 = 9 * (x + 6)
or 8 * 6 / 9 = x + 6
ie x = 8 * 6 / 9 - 6 = 5.333 - 6