Question

How do you solve `\frac { x + 4} { x - 4} = \frac { 6} { 5}`?

Answer 1

Remove the fractions by multiplying by the least common multiple and then simplify and solve.

`x = 44`

Explanation:

First multiply both sides by `5xx(x-4)`, which is the product of both denominators. (`LCD`)

`(5(x-4)xx (x +4))/((x-4)) = (5(x-4) xx 6)/5`

The denominators divide ( or cancel) out:

`(5cancel((x-4)) xx (x +4))/cancel((x-4)) = (cancel5(x-4) xx 6)/cancel5`

leaving only numbers on the top or numerators. This leaves.

`5 xx ( x +4) = ( x -4) xx 6`

Using the distributive property gives.

`5x + 20 = 6x - 24`

Add `24` to both sides to work backwards to find `x`. This gives:

`5x + 20 + 24 = 6x - 24 + 24" "(-24 + 24 = 0)` resulting in:

`5x + 44 = 6x" "` Subtract `5x` from both sides to isolate `x`

`-5x + 5x + 44 = 6x - 5x" " (6x - 5x = 1x )` so the result is:

`44 = x`

Answer 2

`x = 44`

Explanation:

Cross multiply because there is one fraction on each side.

`5 (x+ 4) = 6(x- 4)`

`5x + 20 = 6x - 24`

Collect like terms

`6x - 5x = 20 + 24`

`x = 44`