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22 Apr 2018, 22:08
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A
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Difficulty:
15%
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Question Stats:
76% (01:27) correct
24%
(02:08)
wrong
based on 165
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Which of the following is equivalent to \(\frac{\frac{1}{2x} - \frac{x}{2}}{\frac{1}{x}+1}\)?
A. (1 − x)/2
B. (x − 1)/2
C. (x^2 − 1)/(2x)
D. (1 − x^2)/(2x)
E. 2x/(1 − x^2)
A. (1 − x)/2
B. (x − 1)/2
C. (x^2 − 1)/(2x)
D. (1 − x^2)/(2x)
E. 2x/(1 − x^2)
22 Apr 2018, 22:49
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Bunuel
Ans A... Pls refer the attachment..
Attachment:
IMG_20180423_111837.jpg [ 60.65 KiB | Viewed 3762 times ]
Sent from my ONEPLUS A5010 using GMAT Club Forum mobile app
23 Apr 2018, 10:29
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Bunuel
I would separate numerator and denominator, simplify with shortcuts*, then merge them
Numerator:
\((\frac{1}{2x} - \frac{x}{2})=\frac{1*2-2x*x}{2*2x}=\frac{2-2x^2}{4x}\)
Denominator:
\((\frac{1}{x}+1)=(\frac{1}{x}+\frac{1}{1})=\frac{1*1+x*1}{x*1}=\frac{1 + x}{x}\)
The term \((1+x)\) is a big hint to simplify the original numerator. Answers show that a decent bit needs to be factored out.
\(\frac{2-2x^2}{4x}=\frac{2(1-x^2)}{4x}\)
\((1 - x^2)\) is a difference of squares.**
Numerator, simplified: \(\frac{2(1+x)(1-x)}{4x}\)
Combined again:
\(\frac{\frac{2(1+x)(1-x)}{4x}}{\frac{1 + x}{x}}=(\frac{2(1+x)(1-x)}{4x}*\frac{x}{(1+x)})=\)
\(\frac{(2)(1+x)(1-x)(x)}{(4x)(1+x)}=\frac{(1-x)}{2}\)
Answer A
*Shortcuts: the shortcut to add / subtract fractions is not all that well-known in the U.S. (I've been polling). It saves a lot of time. Use judiciously. At times LCM is better. Shortcut: Add and subtract fractions the easy way
**\((a^2-b^2)=(a+b)(a-b)\)
