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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## What is the solution of the equation (x-1)/(1-x) = 0? tagged by: Max@Math Revolution ##### This topic has 3 expert replies and 0 member replies ### GMAT/MBA Expert ## What is the solution of the equation (x-1)/(1-x) = 0? ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult [Math Revolution GMAT math practice question] What is the solution of the equation (x-1)/(1-x) = 0? A. -1 B. 0 C. 1 D. 0 or 1 E. The equation has no solution. _________________ Math Revolution Finish GMAT Quant Section with 10 minutes to spare. The one-and-only Worldâ€™s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. Only$99 for 3 month Online Course
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Max@Math Revolution wrote:
[Math Revolution GMAT math practice question]

What is the solution of the equation (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 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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Max@Math Revolution wrote:
[Math Revolution GMAT math practice question]

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

A. -1
B. 0
C. 1
D. 0 or 1
E. The equation has no solution.
In order for a fraction to be equal to 0, its numerator must be 0. So x - 1 = 0. This gives us x = 1. However, since the denominator also equals 0 when x = 1, we have division by 0, which is not defined. Therefore, x canâ€™t be 1. In that case, there are no values of x that makes the fraction (x-1)/(1-x) equal to 0.

Alternate solution:

Recall that (a - b)/(b - a) = -1 so long as a â‰  b. Therefore, (x-1)/(1-x) = -1 so long as x â‰  1. Since x canâ€™t be 1 (otherwise the fraction would be undefined). Therefore, (x-1)/(1-x) can never be 0 for any values of x.

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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.

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