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Algebra - Solving Equations

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Algebra - Solving Equations

by [email protected] » Sat Apr 09, 2016 6:46 am
The explanation to the solution of this question in the OG 2016 is not clear. Please help with a clearer explanation.

(X+1/X-1)^2

If X does not equal 0 or 1, and if X is replaced by 1/X everywhere in the above expression, then the resulting expression is equivalent to

A. (X+1/X-1)^2

B. (X-1/X+1)^2

C. (X^2+1)/(1-X^2)

D. (X^2-1)/(X^2+1)

E. -(X-1/X+1)^2
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by [email protected] » Sat Apr 09, 2016 8:48 am
Hi laiyemoa,

There's a full discussion of this question here:

https://www.beatthegmat.com/if-x-not-equ ... 59914.html

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by GMATGuruNY » Sat Apr 09, 2016 8:51 am

(x+1)^2/(X-1)^2

If x is not = 0 or 1, and if x is replaced by 1/x everywhere in the expression above, then the resulting expression is equivalent to?

A) (x+1)^2/(x-1)^2
B) (x-1)^2/(x+1)^2
C) x^2+1/1-X^2
D) X^2-1/X^2+1
E) -(x-1)^2/-(X+1)^2
Let x=2, implying that -- everywhere in the given expression -- x must be replaced by 1/x = 1/2.

Replacing x with 1/2, we get:
(1/2 + 1)²/(1/2 - 1)² = (3/2)²/(-1/2)² = (9/4)/(1/4) = 9. This is our target.

Now plug x=2 into the answer choices to see which yields our target of 9.
A quick scan of the numerators reveals that only A is viable:
(x+1)²/(x-1)² = (2+1)²/(2-1)² = 9.

The correct answer is A.
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