Bunuel wrote:

Which of the following CANNOT be a value of \(\frac{1}{x-1}\)?

A. -1

B. 0

C. 2/3

D. 1

E. 2

Alternatively, we can

test each answer choiceA) -1

Is it possible for 1/(x-1) to equal -1?

Let's find out.

We'll see if we can solve the equation: 1/(x-1) = -1

Multiply both sides by (x-1) to get: 1 = -1(x-1)

Expand right side: 1 = -x + 1

Solve: x = 0

So, when x = 0, 1/(x-1) = -1

Since 1/(x-1) CAN equal -1, we can ELIMINATE A

B) 0

Is it possible for 1/(x-1) to equal 0?

Let's find out.

We'll see if we can solve the equation: 1/(x-1) = 0

Multiply both sides by (x-1) to get: 1 = 0

Hmmmm.

Looks like 1/(x-1) CANNOT equal 0

At this point, I'd select B and move on.

But, for "kicks" let's keep going

C) 2/3

Start with the equation: 1/(x-1) = 2/3

Multiply both sides by (x-1) to get: 1 = (2/3)(x-1)

Expand right side: 1 = 2x/3 - 2/3

Add 2/3 to both sides: 5/3 = 2x/3

Multiply both sides by 3 to get: 5 = 2x

Solve: x = 2.5

So, when x = 2.5, 1/(x-1) = 2/3

Since 1/(x-1) CAN equal 2/3, we can ELIMINATE C

D) 1

Start with the equation: 1/(x-1) = 1

Multiply both sides by (x-1) to get: 1 = (1)(x-1)

Expand right side: 1 = x - 1

Add 1 to both sides: 2 = x

So, when x = 2, 1/(x-1) = 1

Since 1/(x-1) CAN equal 1, we can ELIMINATE D

E) 1

Start with the equation: 1/(x-1) = 2

Multiply both sides by (x-1) to get: 1 = (2)(x-1)

Expand right side: 1 = 2x - 2

Add 2 to both sides: 3 = 2x

Solve: x = 3/2

So, when x = 3/2, 1/(x-1) = 2

Since 1/(x-1) CAN equal 2, we can ELIMINATE E

Answer: E

Cheers,

Brent

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Brent Hanneson – GMATPrepNow.com

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