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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$149 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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