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

Question

Tough and Tricky questions: Algebra.

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

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

Kudos for a correct  solution .

82vkgmat · Accepted Answer

Answer = C.
IMO simple way to look at this is if x = 2, -2 or 1, then one of the fractions listed becomes invalid. So none of these can be answers. That leaves us with -1 or 0.
Plug in each of these. I started with 0 first as it is easiest
LHS = -1/2
RHS = 1/2-1/1 = -1/2. 
LHS = RHS, hence x=0.
Answer: C.

PareshGmat · Answer

Answer = C = 0

\frac{1}{x - 2} = \frac{1}{x + 2} + \frac{1}{x - 1}

\frac{1}{x-1} = \frac{1}{x-2} - \frac{1}{x+2}

\frac{1}{x-1} = \frac{x+2-(x-2)}{x^2 - 4}

\frac{1}{x-1} = \frac{4}{x^2 - 4}

x^2 - 4 = 4x - 4

x = 0 OR x = 2

If we take x = 2; LHS becomes void

hence x = 0

devmillenium2k · Answer

Just put the value of x from the given options and check 
we can verify equation is valid only for x=0

Hence C

Bunuel · Answer

Official Solution:

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

A. -2
B. -1
C. 0
D. 1
E. 2
 
The fastest way to solve this problem is first to recognize that an algebraic approach will take a little time. Essentially, we will have to multiply through by the product  (x - 2)(x + 2)(x - 1) , then simplify.
 
If, instead, we glance at the answer choices, we see that 3 of them make one of the denominators zero, a result that is not allowed (we cannot divide by zero). Specifically,  x  cannot be -2 because one denominator is  x + 2 ; likewise,  x  cannot be 1 or 2, since we have  x - 1  and  x - 2  as denominators as well.
 
Thus, the only two possible answers are -1 and 0. We try each in turn.
 
If  x = -1 , then we have the following:
 
 \frac{1}{-3} = \frac{1}{1} + \frac{1}{-2} ?
 
 -\frac{1}{3} = 1 - \frac{1}{2} ?
 
This is not true.
 
However, if  x = 0 , then we have the following:
 
 \frac{1}{-2} = \frac{1}{2} + \frac{1}{-1} ?
 
 -\frac{1}{2} = \frac{1}{2} - 1 ?
 
 -\frac{1}{2} = -\frac{1}{2} ?
 
This is true, so  x  can be equal to 0.
 
Alternatively, we could take the algebraic approach.
 
First, we multiply through by the product  (x - 2)(x + 2)(x - 1)  to eliminate denominators.
  (x - 1)(x + 2) = (x - 2)(x - 1) + (x - 2)(x + 2) 
  x^2 + x - 2 = x^2 - 3x + 2 + x^2 - 4 
  0 = x^2 - 4x 
  0 = x(x - 4) 
 
 x = 0  or  x = 4 
 
Answer: C.

ehsan090 · Answer

There is always 2 method to solve these question in most cases either putting values or solving equation...
I need expert opinion which is the fastest way to do it 
I usually find putting values fastest not sure about precision what you people say?

matthewsmith_89 · Answer

An easy approach to solve the problem is process elimination.
If we use 0 for x

1/0 - 2 = 1/0+2 + 1/0-1
1/-2 = 1/2 + 1/-1
-1/2 = -1/2

Try the other answers and you will see the answers do not coincide.

The answer is C

daboo343 · Answer

By substituting the value we 0 will satisfy the given equation
Hence C

danbrown9445 · Answer

I dont see how x = 2.

x^2 - 4 = 4x - 4 
  x^2 = 4x  
 x(x-4) = 0

x = 0 or x = 4  NOT  x = 2 or x = 0

vichitravir · Answer

An easy way will be to go with the options.
Put the values of x from the options and verify for the correct answer.

MBAB123 · Answer

Also, to add - you only have to evaluate 2 options - B and C. All the other options would make one of the terms undefined (0 in the denominator).

calj03 · Answer

I'm no expert but here's my train of thoughts:

Right from the get go, I noticed that x can not equal 2; -2; 1 because that would result in operation where we divide by zero which is undefined.

This effectively leaves us with only 2 viable options --> we plug in values.

If we plug 0 for x in the equation, we get:
-1/2 = 1/2 - 1/1
-1/2 = -1/2 which means we found a valid solution. Plugging in -1 for x would result in invalid solution such as -1/3 = 1/2, hence, 0 is the correct answer found within a minute.

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

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GMAT Problem Solving (PS) Questions

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

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