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# sqrt3 + 1/3+sqrt3 - 1/3-sqrt3

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Manager
Joined: 26 Feb 2013
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sqrt3 + 1/3+sqrt3 - 1/3-sqrt3 [#permalink]

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29 Nov 2013, 05:25
$$sqrt3 + \frac{1}{3+sqrt3} - \frac{1}{3-sqrt3}$$

Can someone please suggest ways of solving such problems?
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Joined: 02 Sep 2009
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Kudos [?]: 79312 [0], given: 10016

Re: sqrt3 + 1/3+sqrt3 - 1/3-sqrt3 [#permalink]

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29 Nov 2013, 05:56
Skag55 wrote:
$$sqrt3 + \frac{1}{3+sqrt3} - \frac{1}{3-sqrt3}$$

Can someone please suggest ways of solving such problems?

$$sqrt3 + \frac{1}{3+sqrt3} - \frac{1}{3-sqrt3}=sqrt3 + \frac{(3-sqrt3)-(3+sqrt3)}{(3+sqrt3)(3-sqrt3)}=\sqrt3 + \frac{-2\sqrt3}{9-3}=\sqrt3- \frac{\sqrt3}{3}=\sqrt3-\frac{1}{\sqrt3}=\frac{2}{\sqrt{3}}$$.

Hope it's clear.
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Re: sqrt3 + 1/3+sqrt3 - 1/3-sqrt3   [#permalink] 29 Nov 2013, 05:56
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# sqrt3 + 1/3+sqrt3 - 1/3-sqrt3

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