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

${x}_{1} = 2$ and ${x}_{2} = - 5$

#### Explanation:

LCD$= 3 \left(x - 1\right) \left(x + 1\right)$ and dividing both sides of the equation by 2.

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

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

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

Multiply both sides of the equation by the LCD then simplify

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

$\left[3 \left(x + 1\right) - \left(x - 1\right) \left(x + 1\right)\right] = 6 \left(x - 1\right)$

$3 x + 3 - {x}^{2} + 1 = 6 x - 6$

${x}^{2} + 3 x - 10 = 0$

Solve the quadratic by factoring method

${x}^{2} + 3 x - 10 = 0$

$\left(x - 2\right) \left(x + 5\right) = 0$

$\left(x - 2\right) = 0$ and $\left(x + 5\right) = 0$

${x}_{1} = 2$ and ${x}_{2} = - 5$

God bless....I hope the explanation is useful.