# How do you solve (5x)/(x-1)+5=15/(x-1)?

Sep 29, 2016

$x = \textcolor{g r e e n}{2}$

#### Explanation:

Given
$\textcolor{w h i t e}{\text{XXX}} \frac{5 x}{x - 1} + 5 = \frac{15}{x - 1}$

Multiply both sides by $\left(x - 1\right)$
$\textcolor{w h i t e}{\text{XXX}} 5 x + 5 x - 5 = 15$

$\textcolor{w h i t e}{\text{XXX}} \rightarrow 10 x = 20$

$\textcolor{w h i t e}{\text{XXX}} \rightarrow x = 2$

Sep 29, 2016

I found: $x = 2$
We can choose $x - 1$ as common denominator and write:
$\frac{5 x + 5 \left(\textcolor{red}{x - 1}\right)}{x - 1} = \frac{15}{x - 1}$
$5 x + 5 x - 5 = 15$
$10 x = 20$
$x = \frac{20}{10} = 2$