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

Aug 15, 2016

$11 x - 5 = 0$ does not factor, but can be solved to give $x = \frac{5}{11}$

#### Explanation:

We will need to simplify first. This is not in any recognisable form for factoring.

$\frac{2}{3} = 2 - \frac{5 x - 3}{x - 1} \text{ } \textcolor{b l u e}{\times 3 \left(x - 1\right)}$

Get rid of the denominators:

2/cancel3color(blue)(xx cancel3(x-1)) = 2color(blue)(xx 3(x-1)) - (5x-3)/cancel((x-1)) color(blue)(xx 3cancel((x-1))

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

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

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

This simplifies to a simple linear equation and does not factorise.

$11 x = 5$