[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.
What is the solution of the equation (x-1)/(1-x) = 0?
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- Max@Math Revolution
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Important conceptual question. Congrats, Max!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.
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.
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- Scott@TargetTestPrep
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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 can't be 1. In that case, there are no values of x that makes the fraction (x-1)/(1-x) equal to 0.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.
Alternate solution:
Recall that (a - b)/(b - a) = -1 so long as a ≠b. Therefore, (x-1)/(1-x) = -1 so long as x ≠1. Since x can't be 1 (otherwise the fraction would be undefined). Therefore, (x-1)/(1-x) can never be 0 for any values of x.
Answer: E
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- Max@Math Revolution
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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.
Therefore, the answer is E.
Answer: E
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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