Question

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

Answer 1

Place on the same denominator and solve.

Explanation:

the LCD (least common denominator) is `x^2 - 4`

`(x^2) /((x - 2)(x + 2)) = (x(x - 2))/((x +2)(x - 2))- (-(2(x + 2))/((2 - x)(x - 2)))`

We can eliminate the denominators:

`x^2 = x^2 - 2x - (-2x - 4)`

`x^2 = x^2 - 2x + 2x + 4`

Everything eliminates themselves, so there is no solution.