# How do you solve \frac { 4} { x + 3} = \frac { 2} { x - 3}?

Aug 5, 2018

color(violet)(x = 9

#### Explanation:

$\frac{4}{x = 3} = \frac{2}{x - 3}$

$4 \left(x - 3\right) = 2 \left(x + 3\right) , \text{cross multiplying}$

$4 x - 12 = 2 x + 6 , \text{ removing braces}$

$4 x - 2 x = 6 + 12 , \text{ bringing like terms together}$

$2 x = 18 \text{ or "x = 9, " simplifying}$

Aug 5, 2018

Work backwards to isolate x

#### Explanation:

First remove the parenthesis represented by the division signs

$\left(x + 3\right) \times \left(x - 3\right) \times \frac{4}{x + 3} = \left(x + 3\right) \times \left(x - 3\right) \times \frac{2}{x - 3}$

This gives

$\left(x - 3\right) \times 4 = \left(x + 3\right) \times 2$

multiplying across the parenthesis using the distributive property

$4 x - 12 = 2 x + 6$

Next adding the opposites looks like this

$4 x - 12 + 12 - 2 x = 2 x - 2 x + 12 + 6$

Which gives

$2 x = 18$

divide both sides by 2

$2 \frac{x}{2} = \frac{18}{2}$

$x = 9$