PS - X in Fractions

Re-posting initial question due to character display error.

If 1/(x - 2) = 1/(x + 2) + 1/(x - 1), which of the following is a possible value of x?

(A) -2
(B) -1
(C) 0
(D) 1
(E) 2

Working the problem, I got the solution 0 and 2. But since 2 would make the denominator 0, is that why 0 would be the answer and hence choice C. Did someone get another answer/explanation other than C?

For these types of questions, plugging in numbers is the best way.

If you plug in 0, the solution will be 0. So, this is the possible value of x.