Question

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

Answer 1

This identity will result in:
`x^2/(x^2-4)= (x^2+4)/(x^2-4)` so the solution does not exist...
Why?`x^2/(x^2-4) color(red)ne (x^2+4)/(x^2-4)`
Check your question again...

Explanation:

Given: `x^2/(x^2-4) = x/(x+2)-2/(2-x)`
Find the solution?
First let work on the RHS (Right Hand Side) to add the two terms
`RHS = (x(2-x)-(2x+4))/(-x^2+4) = (-x^2-4)/(-x^2+4)`
multiply both Denominator and Nominator by negative 1:
`RHS= (x^2+4)/(x^2-4)` clearly RHS is not equal to LHS so the solution to this one does not exist. So either you must made an error in writing down your question or you don't have a solution.