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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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    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?2012-09-02

1 Answers 1

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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.2012-09-02