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

Jul 13, 2017

color(magenta)(x=5/11= extraneous solution

#### Explanation:

$\frac{2}{3} = 2 - \frac{5 x - 3}{x - 1}$

$\therefore - \frac{5 x - 3}{x - 1} = \frac{2}{3} - 2$

multiply both sides by $- 1$

$\therefore \frac{5 x - 3}{x - 1} = - \frac{2}{3} + 2$

multiply both sides by $x - 1$

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

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

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

$\therefore 3 \frac{2}{3} x = 3 \frac{2}{3} - 2$

$\therefore \frac{11}{3} x = 3 \frac{2}{3} - 2$

$\therefore \frac{11}{3} x = 1 \frac{2}{3}$

$\therefore \frac{11}{3} x = \frac{5}{3}$

$\therefore x = \frac{\frac{5}{3}}{\frac{11}{3}}$

$\therefore x = \frac{5}{\cancel{3}} ^ 1 \times {\cancel{3}}^{1} / 11$

:.color(magenta)(x=5/11= extraneous solution