Question

How do you solve `6/(x-4) = 5/2`?

Answer 1

`x = 32/5`

Explanation:

First of all, your equation is not defined if any denominator is equal to `0`. Thus,

`x - 4 != 0 <=> x != 4 " "` must hold.

Now, your first step would be to "get rid" of the denominators. To do so, you should multiply both sides of the equation with `x - 4` and `2`:

`color(white)(x) 6 / (x-4) = 5/2`

`<=> (6* (x-4) * 2)/(x-4) = (5 * (x-4) * 2) / 2`

`<=> (6* cancel((x-4)) * 2)/(cancel(x-4)) = (5 * (x-4) * cancel(2)) / cancel(2)`

`<=> 6* 2 = 5(x-4)`

`<=> 12 = 5x-20`

... add `20` on both sides...

`<=> 32 = 5x`

... divide by `5` on both sides...

`<=> 32/5 = x`

So, your solution is `x = 32/5`.