Question

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

Answer 1

I found no solutions (the left side is NOT equal to the right one)

Explanation:

Let us write it as:
`x^2/(x^2-4)=x/(x+2)color(red)(+2/(x-2))`
we can use as common denominator `(x^2-4)` which is equal to `(x+2)(x-2)` and write:
`x^2/cancel((x^2-4))=(x(x-2)+2(x+2))/cancel((x^2-4))`
giving:
`cancel(x^2)=cancel(x^2)cancel(-2x)+cancel(2x)+4`

so we get `4=0` which is not true