Question

How do you solve `(x-4)/(x-2) = (x-2)/(x+2) + (1)/(x-2)`?

Answer 1

`x-4 = ((x-2)(x-2))/(x+2) + 1`
`(x-4)(x+2) = (x-2)(x-2) + (x+2)`
`x^2 - 2x - 8 = x^2-4x+4 + x + 2`

Simplify
`2x - 12 = x + 2`
`x = 14`

Explanation:

The easiest way to do this type of calculation is to get rid of all the denominators. To do this, first times every single term by `x-2`, then do the same, but with `x+2`. At that point, it becomes a matter of simplification.