TITLE: Find mistake in simplifying rational expression
QUESTION [6 upvotes]: Why can't I simplify the following expression?
$$\frac{-(-\frac{\sqrt2}{2})}{(-\frac{\sqrt2}{2})^2}$$
I did this:
$$\frac{-(-\frac{\sqrt2}{2})}{(-\frac{\sqrt2}{2})^2}=\frac{-1(-\frac{\sqrt2}{2})}{(-\frac{\sqrt2}{2})^2}=\frac{-1}{(-\frac{\sqrt2}{2})}=\frac{2}{\sqrt2}$$
However, the correct way to do is first raise a square and then simplify:
$$\frac{-(-\frac{\sqrt2}{2})}{(-\frac{\sqrt2}{2})^2} = \frac{-(-\frac{\sqrt2}{2})}{\frac{2}{4}}=\frac{\sqrt2}{2}\cdot\frac{4}{2}=\sqrt2$$

REPLY [3 votes]: You are dividing two positive numbers so the result is positive. 
Upon simplification of $$ \frac{-(-\frac{\sqrt2}{2})}{(-\frac{\sqrt2}{2})^2}$$ we come up with $$ \frac {1}{ \frac {\sqrt 2}{2}} =\frac {2}{ \sqrt 2}=\sqrt 2$$