Answer
$\dfrac{1}{\sqrt{5}-1}$
Work Step by Step
Multiplying by the conjugate of the numerator, the rationalized-numerator form of the given expression, $
\dfrac{\sqrt{5}+1}{4}
,$ is
\begin{array}{l}\require{cancel}
\dfrac{\sqrt{5}+1}{4}\cdot\dfrac{\sqrt{5}-1}{\sqrt{5}-1}
\\\\=
\dfrac{(\sqrt{5})^2-(1)^2}{4(\sqrt{5})+4(-1)}
\\\\=
\dfrac{5-1}{4\sqrt{5}-4}
\\\\=
\dfrac{4}{4\sqrt{5}-4}
\\\\=
\dfrac{4}{4(\sqrt{5}-1)}
\\\\=
\dfrac{\cancel{4}}{\cancel{4}(\sqrt{5}-1)}
\\\\=
\dfrac{1}{\sqrt{5}-1}
.\end{array}
