# How do you solve the rational equation 5 / (x+4) = 4 + 3/ (x-2)?

Jun 9, 2018

$x = 1$ or x=-5/2#

#### Explanation:

Multiplying the whole equation by $\left(x - 2\right) \left(x + 4\right) \ne 0$
we get
$5 \left(x - 2\right) = 4 \left(x - 2\right) \left(x + 4\right) + 3 \left(x + 4\right)$
expanding
$5 x - 10 = 4 {x}^{2} + 8 x - 32 + 3 x + 12$

$0 = 4 {x}^{2} + 6 x - 10$

$0 = {x}^{2} + \frac{3}{2} x - \frac{5}{2}$

${x}_{1 , 2} = - \frac{3}{4} \pm \sqrt{\frac{9}{16} + \frac{40}{16}}$
so
$x = 1$
or

$x = \frac{5}{2}$