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

1 Answer
May 20, 2017

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.