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I am really stumped as to how it simplifies. I should know this, but it has been a very, very, long summer.

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Have you tried dividing the numerator and denominator by $2$? – Alex Becker Sep 2 '12 at 3:59
I am a bit sad that Austin has edited this post. I only upvoted it because the original rendering of the formula was so amusing. – MJD Sep 2 '12 at 4:04
It looked rather like it was written in lipstick on a white T-shirt. Were you expecting it to simplify down to give some woman's phone number? – user22805 Sep 2 '12 at 4:35
up vote 5 down vote accepted

Pull out a factor of $2$ and cancel:

$$ \begin{align*} \frac{4-2\sqrt{2}}{4} &= \frac{2(2 - \sqrt{2})}{2 \cdot 2}\\ &= \frac{2}{2}\cdot \frac{2-\sqrt{2}}{2}\\ &= 1 \cdot \frac{2-\sqrt{2}}{2}\\ &= \frac{2-\sqrt{2}}{2} \end{align*} $$

Notice we didn't do anything special with the $\sqrt{2}$; it may as well have just been an $x$.

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Hey thanks a lot. – Kyle H Sep 2 '12 at 4:04

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