Rationalise the denominator of the given fraction and present your answer in the…

MATHEMATICS · Multi-part · AoPS · Mathematics · Special Factorizations · Special Factorizations

Problem

Rationalise the denominator of the given fraction and present your answer in the simplest radical form. (i) Find the simplified form of

\displaystyle\frac{1}{3+\sqrt{5}}

after rationalising the denominator. (ii) Verify that the denominator in your final answer is a rational number.