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What is the solution of the equation (x-1)/(1-x) = 0?

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Math Revolution GMAT Instructor
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What is the solution of the equation (x-1)/(1-x) = 0?  [#permalink]

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New post 11 Oct 2018, 01:39
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[Math Revolution GMAT math practice question]

What is the solution of the equation \(\frac{(x-1)}{(1-x)} = 0?\)

\(A. -1\)
\(B. 0\)
\(C. 1\)
\(D. 0\) or \(1\)
E. The equation has no solution.

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Re: What is the solution of the equation (x-1)/(1-x) = 0?  [#permalink]

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New post 11 Oct 2018, 07:45
1
MathRevolution wrote:
[Math Revolution GMAT math practice question]

What is the solution of the equation \(\frac{(x-1)}{(1-x)} = 0?\)

\(A. -1\)
\(B. 0\)
\(C. 1\)
\(D. 0\) or \(1\)
E. The equation has no solution.

Important conceptual question. Congrats, Max!

BEFORE any manipulation/calculation is done, the "mathematical entity" (in this case, the fraction) must EXIST.

Hence we must impose the denominator different from zero, i.e., x different from 1.

We know that any fraction given (if it exists) is zero if, and only if, its numerator is zero.

Only x=1 satisfies that (x-1 = 0 implies x=1).

From the fact that x=1 is not allowed, the equation given has no solutions!


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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Re: What is the solution of the equation (x-1)/(1-x) = 0?  [#permalink]

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New post 11 Oct 2018, 09:00
MathRevolution wrote:
[Math Revolution GMAT math practice question]

What is the solution of the equation \(\frac{(x-1)}{(1-x)} = 0?\)

\(A. -1\)
\(B. 0\)
\(C. 1\)
\(D. 0\) or \(1\)
E. The equation has no solution.

\(\frac{(x-1)}{(1-x)} = 0\)

Or, \(x - 1 = 0\)

So, \(x = 1\)

If \(x = 1\) ; \(\frac{(x-1)}{(1-x)} = \frac{1 - 1}{1 - 1}\) Now, here denominator can not be 0 as anything divided by 0 is Undefined...

Lets try with \(x = 0\) ; \(\frac{(x-1)}{(1-x)} = \frac{0 - 1}{1 - 0} = -1 ≠ 0\)

Lets try with \(x = -1\) ; \(\frac{(x-1)}{(1-x)} = \frac{-1 - 1}{1 + 1} = -1 ≠ 0\)

Thus, the equation has no solution, the answer must be (E) The equation has no solution.
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Re: What is the solution of the equation (x-1)/(1-x) = 0?  [#permalink]

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New post 14 Oct 2018, 18:51
=>

In order for a fraction to be zero, its numerator must be \(0\). This occurs when \(x = 1\). However, if \(x = 1\), then the denominator of this fraction is \(0\). Thus, \(0\) is an erroneous solution, and the equation has no solution.

Therefore, the answer is E.
Answer: E
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Re: What is the solution of the equation (x-1)/(1-x) = 0?   [#permalink] 14 Oct 2018, 18:51
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