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

Jun 10, 2017

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

#### Explanation:

$\frac{2}{x - 1} - \frac{2}{3} = \frac{4}{x + 1}$. Multiplying by $3 \left(x - 1\right) \left(x + 1\right)$ on both side we get, $2 \cdot 3 \cdot \left(x + 1\right) - 2 \left({x}^{2} - 1\right) = 4 \cdot 3 \cdot \left(x - 1\right)$ or

$6 x + 6 - 2 {x}^{2} + 2 = 12 x - 12 \mathmr{and} 2 {x}^{2} + 12 x - 6 x - 12 - 8 = 0$ or

$2 {x}^{2} + 6 x - 20 = 0 \mathmr{and} {x}^{2} + 3 x - 10 = 0 \mathmr{and} {x}^{2} + 5 x - 2 x - 10 = 0$ or

$x \left(x + 5\right) - 2 \left(x + 5\right) = 0 \mathmr{and} \left(x + 5\right) \left(x - 2\right) = 0 \therefore$either $x - 2 = 0 \therefore x = 2$ or
$x + 5 = 0 \therefore x = - 5$

Solution : $x = 2 \mathmr{and} x = - 5$ [Ans]