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\sqrt{5}+\frac{\sqrt{5}}{\left(\sqrt{5}\right)^{2}}
Rationalize the denominator of \frac{1}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.
\sqrt{5}+\frac{\sqrt{5}}{5}
The square of \sqrt{5} is 5.
\frac{6}{5}\sqrt{5}
Combine \sqrt{5} and \frac{\sqrt{5}}{5} to get \frac{6}{5}\sqrt{5}.