It is currently 22 Apr 2019, 14:23

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Which of the following is equal to

Author Message
TAGS:
Founder
Joined: 18 Apr 2015
Posts: 6215
Followers: 99

Kudos [?]: 1201 [0], given: 5727

Which of the following is equal to [#permalink]  14 Sep 2017, 07:07
Expert's post
00:00

Question Stats:

100% (00:32) correct 0% (00:00) wrong based on 5 sessions

Which of the following is equal to $$\frac{-2}{\sqrt{n-1} - \sqrt{n+1}}$$ for all values of n > 1?

A. -1

B. 1

C. $$2(\sqrt{n-1} + \sqrt{n+1})$$

D. $$\sqrt{n-1} + \sqrt{n+1}$$

E. $$\frac{\sqrt{n-1}}{\sqrt{n+1}}$$
[Reveal] Spoiler: OA

_________________
Director
Joined: 03 Sep 2017
Posts: 521
Followers: 1

Kudos [?]: 355 [1] , given: 66

Re: Which of the following is equal to [#permalink]  18 Sep 2017, 01:22
1
KUDOS
One way to simplify an expression containing square roots at the denominator is to proceed by rationalization. The dea is to multiply and divide the expression for the same number in order to eliminate the roots at the denominator. In our case,$$\frac{-2}{sqrt(n-1)-sqrt(n+1)}$$ should be multiplied by $$\frac{sqrt(n-1)+sqrt(n+1)}{sqrt(n-1)+sqrt(n+1)}$$ so that at the denominator we get a difference of squares.
Thus, $$\frac{-2}{sqrt(n-1)-sqrt(n+1)}*\frac{sqrt(n-1)+sqrt(n+1)}{sqrt(n-1)+sqrt(n+1)}=\frac{-2*[sqrt(n-1)+sqrt(n+1)]}{(n-1)-(n+1)}=\frac{-2*[sqrt(n-1)+sqrt(n+1)]}{-2}=sqrt(n-1)+sqrt(n+1)$$.

Re: Which of the following is equal to   [#permalink] 18 Sep 2017, 01:22
Display posts from previous: Sort by