If x^2 1, which is equal to x/(x + 1) x/(x 1) + 2/(x^2 1) ?

Question

If x^2 ≠ 1, which is equal to  \frac{x}{(x + 1)} − \frac{x}{(x − 1)} + \frac{2}{(x^2 − 1)} ?

A.  \frac{(−x + 3)}{(x + 1)}

B.  \frac{2}{(x + 1)}

C.  \frac{−2}{(x + 1)}

D.  \frac{2}{(x − 1)}

E.  \frac{−2}{(x − 1)}

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Ayeka · Answer

x/(x+1) - x/(x-1) +2/(x^2 -1) 
Taking LCM
(x(x-1) -x(x+1)+2)/(x^2-1) 
(x^2 -x -x^2 -x+2)/(x+1)(x-1)
(-2x+2)/(x+1)(x-1)
(-2)(x-1)/(x+1)(x-1)
-2/(x+1)

Answer: C

Dereno · Answer

\frac{x}{(x + 1)} − \frac{x}{(x − 1)} + \frac{2}{(x^2 − 1)}

Taking the LCM as (x^2 -1) = (x-1)*(x+1)

=  \frac{x*(x-1)}{(x-1)*(x + 1)} − \frac{x*(x+1)}{(x+1)*(x − 1)} + \frac{2}{(x^2 − 1)}

=   \frac{ -2*x }{ (x+1)*(x-1) } + \frac{ 2}{(x+1)*(x-1) }

=   \frac{ -2*(x-1) }{ (x-1)*(x+1) }

=    \frac{ -2}{(x+1) }

Option C

ManifestDreamMBA · Answer

\frac{x}{(x + 1)} − \frac{x}{(x − 1)} + \frac{2}{(x^2 − 1)} 
 \frac{x(x-1)-x(x+1)}{(x+1)(x − 1)} + \frac{2}{(x^2 − 1)} 
 \frac{x^2-x-x^2-x}{(x^2 − 1)} + \frac{2}{(x^2 − 1)} 
 \frac{-2x+2}{(x^2 − 1)} 
 \frac{-2(x-1)}{(x+1)(x-1)} 
 \frac{-2}{(x+1)}

rohitz98 · Answer

Given https://gmatclub.com/forum/download/file.php?id=84603 simplifying by cross multiplying first terms gives / + 2/(x^2 - 1) Solving we get -2(x-1)/(x^2 - 1) Simplifying we get -2/(x+1) Option C GMAT-Club-Forum-ioslpyyx.png

harjas2222 · Answer

mentioning  Bunuel  for checking

x^2 is not equal to 1
which means x>1

assume x = 2

2/2+1 - 2/1 + 2/2^2-1

2/3 - 2 + 2/3

4/3 - 2

-2/3

we know 3 = x + 1

thus -2/ x + 1

is it the correct approach to this question?

If x^2 1, which is equal to x/(x + 1) x/(x 1) + 2/(x^2 1) ?

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GMAT Problem Solving (PS) Questions

If x^2 1, which is equal to x/(x + 1) x/(x 1) + 2/(x^2 1) ?

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

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My Rewards