Answer
$\sqrt{5}-\sqrt{3}$
Work Step by Step
Multiplying by the conjugate of the denominator and using $(a+b)(a-b)=a^2-b^2,$ the given expression, $
\dfrac{2}{\sqrt{5}+\sqrt{3}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{2}{\sqrt{5}+\sqrt{3}}\cdot\dfrac{\sqrt{5}-\sqrt{3}}{\sqrt{5}-\sqrt{3}}
\\\\=
\dfrac{2(\sqrt{5}-\sqrt{3})}{(\sqrt{5})^2-(\sqrt{3})^2}
\\\\=
\dfrac{2(\sqrt{5}-\sqrt{3})}{5-3}
\\\\=
\dfrac{2(\sqrt{5}-\sqrt{3})}{2}
\\\\=
\dfrac{\cancel{2}(\sqrt{5}-\sqrt{3})}{\cancel{2}}
\\\\=
\sqrt{5}-\sqrt{3}
.\end{array}
