Rationalizing the Denominator

[boseph158]

All I need help with is getting started, it has been awhile since I've done one of these problems. Thanks.

(1)/(1+sqrt(3)-sqrt(5))

 

[galactus]

\(\displaystyle \frac{1}{1+\sqrt{3}-\sqrt{5}}\)


Multiply top and bottom by \(\displaystyle 2\sqrt{15}+\sqrt{5}+3\sqrt{3}+7\)

This will eliminate the radicals in the denominator.

 

[BigGlenntheHeavy]

\(\displaystyle My \ way.\)

\(\displaystyle \frac{1}{1+\sqrt3-\sqrt5}*\frac{1-\sqrt3+\sqrt5}{1-\sqrt3+\sqrt5} \ = \ \frac{1-\sqrt3+\sqrt5}{2\sqrt{15}-7}\)

\(\displaystyle Hence, \ \frac{1-\sqrt3+\sqrt5}{2\sqrt{15}-7}* \ \frac{2\sqrt{15}+7}{2\sqrt{15}+7} \ = \ \frac{7+3\sqrt3+\sqrt5+2\sqrt{15}}{11}\)