Evaluate
\sqrt{6}-1\approx 1.449489743
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\frac{5\left(\sqrt{6}-1\right)}{\left(\sqrt{6}+1\right)\left(\sqrt{6}-1\right)}
Rationalize the denominator of \frac{5}{\sqrt{6}+1} by multiplying numerator and denominator by \sqrt{6}-1.
\frac{5\left(\sqrt{6}-1\right)}{\left(\sqrt{6}\right)^{2}-1^{2}}
Consider \left(\sqrt{6}+1\right)\left(\sqrt{6}-1\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{5\left(\sqrt{6}-1\right)}{6-1}
Square \sqrt{6}. Square 1.
\frac{5\left(\sqrt{6}-1\right)}{5}
Subtract 1 from 6 to get 5.
\sqrt{6}-1
Cancel out 5 and 5.
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