Find mistake in simplifying rational expression

There is nothing wrong, in the sense that both final expressions are equivalent: $$\frac2{\sqrt2}=\frac{\sqrt2\cdot\sqrt2}{\sqrt2}=\sqrt2$$ Yet $\sqrt2$ is simpler, both in number of operations and the lack of an irrational denominator.

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 $$ \frac {1}{ \frac {\sqrt 2}{2}} =\frac {2}{ \sqrt 2}=\sqrt 2$$