Evaluate
\sqrt{5}+5\approx 7.236067977
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\frac{20\left(5+\sqrt{5}\right)}{\left(5-\sqrt{5}\right)\left(5+\sqrt{5}\right)}
Rationalize the denominator of \frac{20}{5-\sqrt{5}} by multiplying numerator and denominator by 5+\sqrt{5}.
\frac{20\left(5+\sqrt{5}\right)}{5^{2}-\left(\sqrt{5}\right)^{2}}
Consider \left(5-\sqrt{5}\right)\left(5+\sqrt{5}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
\frac{20\left(5+\sqrt{5}\right)}{25-5}
Square 5. Square \sqrt{5}.
\frac{20\left(5+\sqrt{5}\right)}{20}
Subtract 5 from 25 to get 20.
5+\sqrt{5}
Cancel out 20 and 20.
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