Question

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

Answer 1

`color(violet)(x = 9`

Explanation:

`4 / (x = 3) = 2 / (x - 3)`

`4(x - 3) = 2 (x + 3), "cross multiplying"`

`4x - 12 = 2x + 6, " removing braces"`

`4x - 2x = 6 + 12, " bringing like terms together"`

`2x = 18 " or "x = 9, " simplifying"`

Answer 2

Work backwards to isolate x

Explanation:

First remove the parenthesis represented by the division signs

`( x +3) xx ( x -3) xx 4/(x+3) = ( x+3) xx ( x -3) xx 2/( x-3)`

This gives

`(x -3) xx 4 = (x +3 )xx 2`

multiplying across the parenthesis using the distributive property

`4x -12 = 2x + 6`

Next adding the opposites looks like this

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

Which gives

`2x = 18`

divide both sides by 2

`2x/2 = 18/2`

`x = 9`