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When asked to rationalize the denominator for $\frac{2}{\sqrt{2}+3}$, I came up with $\frac{6-2\sqrt{2}}{7}$ but my algebra book gives -$\frac{2\sqrt{2}-6}{7}$ as the answer. I think we're both correct or am I missing something here? I'm 99% sure I'm right, but I'm not feeling confident... :P

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    @user6312 Interesting. I'll have to keep that in mind as I go through the rest of the book. Thanks for the insight! It just seemed the most straightforward way to do it to me at the time.2011-04-30

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Suppose you went $6$ units to the right and $2\sqrt{2}$ units to the left, reaching a point $P$. Now suppose you went $2\sqrt{2}$ units to the right and $6$ units to the left, reaching a point $Q$. What's the relation between $P$ and $Q$?

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    Thanks, I always appreciate a different way of looking at it.2011-04-30
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yes, both you and the book are correct.