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\frac{-2\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}
Rationalize the denominator of \frac{-2}{2\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.
\frac{-2\sqrt{2}}{2\times 2}
The square of \sqrt{2} is 2.
\frac{-\sqrt{2}}{2}
Cancel out 2 in both numerator and denominator.