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

Jul 12, 2016

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

#### Explanation:

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

In an equation with fractions, we can get rid of denominators completely by multiplying by the LCM of the denominators. Then the denominators can cancel.

In this case the LCM = $\textcolor{red}{3 \left(x - 1\right)}$

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

$\frac{\cancel{3} \left(x - 1\right) \times 2}{\cancel{3}} = 6 \left(x - 1\right) - \frac{3 \cancel{x - 1} \times \left(5 x - 3\right)}{\cancel{x - 1}}$

$2 \left(x - 1\right) = 6 \left(x - 1\right) - 3 \left(5 x - 3\right)$

$2 x - 2 = 6 x - 6 - 15 x + 9$

$2 x - 6 x + 15 x = - 6 + 9 + 2$

$11 x = 5$

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