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My question is- Simplify:

$\frac{1}{\sqrt{3}+\sqrt{2}} + \frac{2}{\sqrt{5}-\sqrt{3}} - \frac{3}{\sqrt{2}+\sqrt{5}}$

My answer is $2\sqrt{3}$. Am I right? I would also like to know the solution as I am a bit confused about whether to take absolute values while solving it.

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    Say, why is it called rationalizing the denominator anyways? I didn't know that denominators were unreasonable.2014-11-24

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The answer is correct, and no absolute values are necessary.