# How do you solve the rational equation 2/(x+2) = 9/8 - (5x)/(4x+8)?

Mar 24, 2016

Put on an equal denominator.

#### Explanation:

$\frac{2}{x + 2} = \frac{9}{8} + \frac{5 x}{4 \left(x + 2\right)}$

The LCD is (x + 2)(8)

$\frac{2 \times 8}{8 x + 16} = \frac{9 \left(x + 2\right)}{8 x + 16} + \frac{10 x}{8 x + 16}$

We can now eliminate the denominators since all the fractions are equivalent. As a result, we will be left with a simple linear equation.

$16 = 9 x + 18 + 10 x$

$16 - 18 = 19 x$

$- 2 = 19 x$

$- \frac{2}{19} = x$

Hopefully this helps!