\(\frac{1-x}{x-1}=\frac{1}{x}\)

Quantity A	Quantity B
\(x\)	\(\frac{-1}{2}\)

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.





_________________

Get the 2 FREE GREPrepclub Tests

"we already know that x must be different from " from where you already known that?

Aside: from the given equation, we know that x ≠ 0 and we know that x-1 ≠ 0
Here's why:
If x = 0, we get: (1-0)/(0-1) = 1/0
Simplify to get: -1 = 1/0 DOESN'T WORK
So, x ≠ 0

Likewise, if x-1 = 0, then x = 1
If we plug in 1 for x, we get: (1-1)/(1-1) = 1/1
Simplify to get: 0/0 = 1/1 DOESN'T WORK
So, x-1 ≠ 0

--------------------------------
Okay, now for a different approach....

Notice that 1-x = -1(-1 + x) = -1(x-1)
So, let's take (1-x)/(x-1) = 1/x and replace (1-x) with -1(x-1)

We get: -1(x-1)/(x-1) = 1/x
Simplify to get: -1 = 1/x
Solve to get: x = -1

So, we have:
Quantity A: -1
Quantity B: -1/2

Answer: B
_________________

Brent Hanneson – Creator of greenlighttestprep.com

Sign up for our free GRE Question of the Day emails