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# If x is positive, then 1/(root(x+1) + root(x)) =

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Intern
Joined: 16 Nov 2013
Posts: 29
Location: United States
Concentration: Entrepreneurship, General Management
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If x is positive, then 1/(root(x+1) + root(x)) = [#permalink]

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21 Nov 2013, 01:03
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Question Stats:

81% (00:42) correct 19% (01:37) wrong based on 130 sessions

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If x is positive, then $$\frac{1}{\sqrt{x+1}+\sqrt{x}}=$$

A) 1

B) x

C) $$\frac{1}{x}$$

D) $$\sqrt{x+1}-\sqrt{x}$$

E) $$\sqrt{x+1}+\sqrt{x}$$
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 43361
Re: If x is positive, then 1/(root(x+1) + root(x)) = [#permalink]

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21 Nov 2013, 01:11
2
KUDOS
Expert's post
registerincog wrote:
If x is positive, then $$\frac{1}{\sqrt{x+1}+\sqrt{x}}$$

A) 1
B) x
C) $$\frac{1}{x}$$
D) $$\sqrt{x+1}-\sqrt{x}$$
E) $$\sqrt{x+1}+\sqrt{x}$$

Rationalize the fraction by multiplying it by $$\frac{\sqrt{x+1}-\sqrt{x}}{\sqrt{x+1}-\sqrt{x}}$$ and apply $$(a+b)(a-b)=a^2-b^2$$ to the denominator:

$$\frac{1}{\sqrt{x+1}+\sqrt{x}}*\frac{\sqrt{x+1}-\sqrt{x}}{\sqrt{x+1}-\sqrt{x}}=\frac{\sqrt{x+1}-\sqrt{x}}{x+1-x}=\sqrt{x+1}-\sqrt{x}$$.

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Re: If x is positive, then 1/(root(x+1) + root(x)) = [#permalink]

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18 Dec 2013, 04:42
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Am I being stupid, or is the question missing something?

I.e. should there not be a question mark or something at the end, or at least an equal sign.
Math Expert
Joined: 02 Sep 2009
Posts: 43361
Re: If x is positive, then 1/(root(x+1) + root(x)) = [#permalink]

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18 Dec 2013, 05:53
wuhanmatt wrote:
Am I being stupid, or is the question missing something?

I.e. should there not be a question mark or something at the end, or at least an equal sign.

You are right there should be an equal sign at the end. Edited. Thank you.
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WE: Information Technology (Computer Software)
Re: If x is positive, then 1/(root(x+1) + root(x)) = [#permalink]

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11 Sep 2014, 02:01
3
KUDOS
registerincog wrote:
If x is positive, then $$\frac{1}{\sqrt{x+1}+\sqrt{x}}=$$

A) 1
B) x
C) $$\frac{1}{x}$$
D) $$\sqrt{x+1}-\sqrt{x}$$
E) $$\sqrt{x+1}+\sqrt{x}$$

For such type of questions, change the middle sign & reciprocal

For example, $$\frac{1}{\sqrt{6} + \sqrt{5}} = \sqrt{6} - \sqrt{5}$$

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Re: If x is positive, then 1/(root(x+1) + root(x)) = [#permalink]

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05 Oct 2017, 06:21
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If x is positive, then 1/(root(x+1) + root(x)) =   [#permalink] 05 Oct 2017, 06:21
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