If \(\dfrac1{x-2}=\dfrac1{x+2}+\dfrac1{x-1},\) which of the following is a possible value of \(x?\)

[Vincen]

If \(\dfrac1{x-2}=\dfrac1{x+2}+\dfrac1{x-1},\) which of the following is a possible value of \(x?\)

A. -2
B. -1
C. 0
D. 1
E. 2

Answer: C

Source: Manhattan GMAT

[Brent@GMATPrepNow]

If \(\dfrac1{x-2}=\dfrac1{x+2}+\dfrac1{x-1},\) which of the following is a possible value of \(x?\)

A. -2
B. -1
C. 0
D. 1
E. 2

Answer: C

Source: Manhattan GMAT

A super-fast approach is to test the answer choices

IMPORTANT: Our work will be made even faster if we recognize that none of denominators (in the given equation) can equal zero. Otherwise, that fraction will be undefined.
So, we can automatically eliminate answer choices A, D and E, since they will all yield denominators that are equal to 0.

We're left with only answer choices B and C (and we haven't even done any work yet!!!)

Let's test answer choice B
Replace x with -1 to get: 1/[(-1) – 2] = 1/[(-1) + 2] + 1/[(-1) – 1]

Simplify to get: -1/3 = 1/1 + (-1/2)
Doesn't work!!
Eliminate house for choice B.

By the process of elimination, the correct answer is C

Cheers,
Brent