# How do you solve  2/3 = 2 - (5x-3)/(x-1)?

Mar 20, 2018

Arrange the equation and get $x = \frac{5}{11}$

#### Explanation:

$\frac{2}{3} = \frac{2 \left(x - 1\right) - 5 x - 3}{x - 1}$

$2 \left(x - 1\right) = 3 \left\{2 \left(x - 1\right) - \left(5 x - 3\right)\right\}$

$2 x - 2 = 3 \left\{2 x - 5 x - 2 + 3\right\}$

$2 x - 2 = - 9 x + 3$

$2 x + 9 x = 3 + 2$

$11 x = 5$

$x = \frac{5}{11}$