# How do you solve \frac { 15} { x } - 4= \frac { 6} { x } + 3?

Nov 14, 2016

$\textcolor{g r e e n}{x = 1 \frac{2}{7}}$

#### Explanation:

Given
$\textcolor{w h i t e}{\text{XXX}} \frac{15}{x} - 4 = \frac{6}{x} + 3$

Multiply everything on both sides by $x$
$\textcolor{w h i t e}{\text{XXX}} 15 - 4 x = 6 + 3 x$

Add $4 x$ to both sides
$\textcolor{w h i t e}{\text{XXX}} 15 = 6 + 7 x$

Subtract $6$ from both sides
$\textcolor{w h i t e}{\text{XXX}} 9 = 7 x$

Divide both sides by $7$
$\textcolor{w h i t e}{\text{XXX}} \frac{9}{7} = x \rightarrow r = \frac{9}{1} = 1 \frac{2}{7}$