# Simplify this expression with radical signs

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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Answer is right. No absolute values should be used. – André Nicolas Jun 8 '12 at 14:16
You're probably thinking of your previous question, where there were expressions of the form $\sqrt{A^2}$. In that case, it's true that $\sqrt{A^2}=|A|$, but now of course that appears nowhere here. – rschwieb Jun 8 '12 at 14:24
@meg_1997: I assume you did the problem by rationalizing the denominators separately. If you used another way, say so, rationalizing denominators gives a simple solution. – André Nicolas Jun 8 '12 at 14:30
Say, why is it called rationalizing the denominator anyways? I didn't know that denominators were unreasonable. – John Joy Nov 24 '14 at 14:39

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

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