Rationalize the denominator and simplify

MATHEMATICS · Single correct · AoPS · Mathematics · Special Factorizations · Special Factorizations

Problem

\dfrac{\sqrt{2}}{3-\sqrt{5}}

. The simplified result is (a)

\dfrac{3\sqrt{2}-\sqrt{10}}{4}

(b)

\dfrac{3\sqrt{2}+\sqrt{10}}{8}

(c)

\dfrac{3\sqrt{2}+\sqrt{10}}{4}

(d)

\dfrac{\sqrt{2}+3\sqrt{5}}{4}