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1-x/x-1=1/x

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1-x/x-1=1/x [#permalink] New post 18 Jan 2016, 08:43
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Question Stats:

41% (00:20) correct 58% (00:45) wrong based on 17 sessions
\(\frac{1-x}{x-1}=\frac{1}{x}\)

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.




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Re: 1-x/x-1=1/x [#permalink] New post 18 Jan 2016, 08:50
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Solution

Since the denominator must be different from zero we do have that x is different from 1 and zero

Multiplying both sides we do have: \(x-x^2=x-1\) from which\(x^2=1\)

Our roots are \(x=1\) or \(x=-1\) but we already know that x must be different from 1. So the only value we do have is \(x=-1\)

\(-1 < \frac{1}{2}\)

The answer is \(B\)
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Re: 1-x/x-1=1/x [#permalink] New post 20 Dec 2016, 10:02
"we already know that x must be different from " from where you already known that?
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Re: 1-x/x-1=1/x [#permalink] New post 20 Dec 2016, 10:13
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Hey,

The relation \(\frac{1-x}{x-1}=\frac{1}{x}\) is already told to be true.

Now if you put x=1 the LHS becomes undefined and and if x=0 then RHS becomes undefined.

Hence X cannot be 0 or 1.
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Re: 1-x/x-1=1/x [#permalink] New post 27 Dec 2016, 09:21
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Carcass wrote:
\(\frac{1-x}{x-1}=\frac{1}{x}\)

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




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
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Re: 1-x/x-1=1/x [#permalink] New post 15 Nov 2017, 23:39
(1-x)/(x-1)=1/x
-1(x-1)/(x-1)=1/x
therefore, x=-1 then qty b=-0.5 so qty b is greater
Re: 1-x/x-1=1/x   [#permalink] 15 Nov 2017, 23:39
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