# How do you solve  6/ (x + 3) = 4/(x - 3)?

Oct 8, 2015

$x = 15$

#### Explanation:

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

Multiplying both sides by $\left(x + 3\right) \left(x - 3\right)$
[2]$\textcolor{w h i t e}{\text{XXX}} \frac{6 \cancel{x + 3} \left(x - 3\right)}{\cancel{x + 3}} = \frac{4 \left(x + 3\right) \left(\cancel{x - 3}\right)}{\cancel{x - 3}}$

[3]$\textcolor{w h i t e}{\text{XXX}} 6 \left(x - 3\right) = 4 \left(x + 3\right)$

Simplifying by distribution
[4]$\textcolor{w h i t e}{\text{XXX}} 6 x - 18 = 4 x + 12$

Add $\left(18 - 4 x\right)$ to both sides
[5]$\textcolor{w h i t e}{\text{XXX}} 2 x = 30$

Divide both sides by $2$
[6]#color(white)("XXX")x=15