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2\sqrt{5}-\frac{2\sqrt{5}}{\left(\sqrt{5}\right)^{2}}
Rationalize the denominator of \frac{2}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.
2\sqrt{5}-\frac{2\sqrt{5}}{5}
The square of \sqrt{5} is 5.
\frac{8}{5}\sqrt{5}
Combine 2\sqrt{5} and -\frac{2\sqrt{5}}{5} to get \frac{8}{5}\sqrt{5}.