# How do you solve 2/(x-1) - 2/3 =4/(x+1)?

Mar 31, 2017

$x = - 5 \mathmr{and} 2$

#### Explanation:

$\frac{2}{x - 1} - \frac{2}{3} = \frac{4}{x + 1}$

$\implies$ $\frac{2}{x - 1} - \frac{4}{x + 1} = \frac{2}{3}$

$\implies$ $\frac{2 \left(x + 1\right) - 4 \left(x - 1\right)}{\left(x - 1\right) \cdot \left(x + 1\right)} = \frac{2}{3}$

$\implies$ $\frac{2 \left(x + 1\right) - 4 \left(x - 1\right)}{{x}^{2} - 1} = \frac{2}{3}$

$\implies$ $\left(6 - 2 x\right) 3 = 2 \left({x}^{2} - 1\right)$
$\implies$ $\left(3 - x\right) 3 = {x}^{2} - 1$
$\implies$${x}^{2} + 3 x - 10 = 0$

[ solution of a general quadratic equation of the form $a {x}^{2} + b x + c = 0$ is given by
$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$]

$\implies$ $x = \frac{- 3 \pm \sqrt{9 + 40}}{2}$
$\implies$$x = \frac{- 3 \pm 7}{2}$
$\implies$$x = - 5 , 2$