Answer
$\dfrac{7}{\sqrt{15}-1}$
Work Step by Step
Multiplying by the conjugate of the numerator, then the rationalized-numerator form of the given expression, $ \dfrac{\sqrt{15}+1}{2} ,$ is \begin{array}{l}\require{cancel} \dfrac{\sqrt{15}+1}{2}\cdot\dfrac{\sqrt{15}-1}{\sqrt{15}-1} \\\\= \dfrac{(\sqrt{15})^2-(1)^2}{2(\sqrt{15})-2(1)} \\\\= \dfrac{15-1}{2\sqrt{15}-2}
\\\\=
\dfrac{14}{2\sqrt{15}-2}
\\\\=
\dfrac{14}{2(\sqrt{15}-1)}
\\\\=
\dfrac{\cancel{2}\cdot7}{\cancel{2}(\sqrt{15}-1)}
\\\\=
\dfrac{7}{\sqrt{15}-1}
.\end{array}
