How do you solve x^2/(x^2-4) = x/(x+2)-2/(2-x)x2x24=xx+222x?

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)x2x24=xx+222x
x^2/(x^2-4)=x/(x+2)-2/(-1*(x-2))x2x24=xx+221(x2)
x^2/(x^2-4)=x/(x+2)+2/(x-2)x2x24=xx+2+2x2
Now, multiply both sides by (x-2)(x+2)(x2)(x+2), since this is the LCM.
Doing this gets:
x^2=x(x-2)+2(x+2)x2=x(x2)+2(x+2)
x^2=x^2-2x+2x+4x2=x22x+2x+4
0=40=4 which is not possible.
There is no solution.