TITLE: how does this simplify?
QUESTION [5 upvotes]: I am really stumped as to how it simplifies. I should know this, but it has been a very, very, long summer.

REPLY [5 votes]: 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 $x$.