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

Jun 25, 2018

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

#### Explanation:

Let's subtract $2$ from both sides to get

$\frac{2}{3} - \frac{6}{3} = - \frac{5 x - 3}{x - 1}$

$\implies - \frac{4}{3} = - \frac{5 x - 3}{x - 1}$

To get rid of the $x - 1$ in the denominator, let's multiply both sides by it. This gives us

$\frac{- 4 \left(x - 1\right)}{3} = - \left(5 x - 3\right)$

We can also get rid of the $3$ in the denominator by multiplying both sides by it. We get

$- 4 \left(x - 1\right) = - 3 \left(5 x - 3\right)$

Let's distribute the $- 4$ and $- 3$ to their respective terms to get

$- 4 x + 4 = - 15 x + 9$

Adding $15 x$ on both sides gives us

$11 x + 4 = 9$

Subtracting $4$ from both sides, we get

$11 x = 5$

Lastly, dividing both sides by $11$ gives us

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

Hope this helps!