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\frac{2\sqrt{10}}{2\left(\sqrt{10}\right)^{2}}
Rationalize the denominator of \frac{2}{2\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.
\frac{2\sqrt{10}}{2\times 10}
The square of \sqrt{10} is 10.
\frac{\sqrt{10}}{10}
Cancel out 2 in both numerator and denominator.