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Which of the following is equal to

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Which of the following is equal to [#permalink] New post 14 Sep 2017, 07:07
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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

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Re: Which of the following is equal to [#permalink] New post 18 Sep 2017, 01:22
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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, \(\frac{-2}{sqrt(n-1)-sqrt(n+1)}*\frac{sqrt(n-1)+sqrt(n+1)}{sqrt(n-1)+sqrt(n+1)}=\frac{-2*[sqrt(n-1)+sqrt(n+1)]}{(n-1)-(n+1)}=\frac{-2*[sqrt(n-1)+sqrt(n+1)]}{-2}=sqrt(n-1)+sqrt(n+1)\).

Thus, the answer is D!
Re: Which of the following is equal to   [#permalink] 18 Sep 2017, 01:22
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Which of the following is equal to

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