Question

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

Answer 1

There is no solution.

Explanation:

First rearrange the equation so that a LCM of the denominator can be obtained.
`x^2/(x^2-4)=x/(x+2)-2/(2-x)`
`x^2/(x^2-4)=x/(x+2)-2/(-1*(x-2))`
`x^2/(x^2-4)=x/(x+2)+2/(x-2)`
Now, multiply both sides by `(x-2)(x+2)`, since this is the LCM.
Doing this gets:
`x^2=x(x-2)+2(x+2)`
`x^2=x^2-2x+2x+4`
`0=4` which is not possible.
There is no solution.