If x is not equal to 1 and y = 1/(x −1), then which one

Gmat_mission wrote:If x is not equal to 1 and $$y=\frac{1}{x-1},$$ then which one of the following cannot be the value of y?

(A) 0
(B) 1
(C) 2
(D) 3
(E) 4

[spoiler]OA=A[/spoiler].

Could someone tell me how to solve this PS question? How can I prove, for example, that y can be equal to 2? I'd appreciate any help.

Hello Gma_mission.

Let's see your question.

First, let's remember that a fraction is zero ONLY when the numerator is equal to zero.

Since "y" is a fraction, then we have to watch its numerator. $$y=\frac{1}{x-1}.$$ Since 1 can never be equal to zero, then "y" never can be equal to zero.

Therefore, the correct answer is the option A.

On the other hand, if we want to know the value of x such that y is equal to 2, then we have to solve the following equation: $$2=\frac{1}{x-1}\ \ \Leftrightarrow\ \ \ x-1=\frac{1}{2}\ \ \ \Leftrightarrow\ \ x=\frac{3}{2}.$$ Hence, when x=3/2, then y=2.

Actually, "y" can be equal to any real number different from zero.