Answer
$\sqrt{7}+\sqrt{5}$
Work Step by Step
Multiplying by the conjugate of the denominator, the given expression, $
\dfrac{2}{\sqrt{7}-\sqrt{5}}
,$ is equivalent to
\begin{align*}\require{cancel}
&
\dfrac{2}{\sqrt{7}-\sqrt{5}}\cdot\dfrac{\sqrt{7}+\sqrt{5}}{\sqrt{7}+\sqrt{5}}
\\\\&=
\dfrac{2(\sqrt{7}+\sqrt{5})}{\left(\sqrt{7}\right)^2-\left(\sqrt{5}\right)^2}
&(\text{use }(a+b)(a-b)=a^2-b^2)
\\\\&=
\dfrac{2(\sqrt{7}+\sqrt{5})}{7-5}
\\\\&=
\dfrac{\cancel2(\sqrt{7}+\sqrt{5})}{\cancel2}
\\\\&=
\sqrt{7}+\sqrt{5}
.\end{align*}
Hence, the expression $
\dfrac{2}{\sqrt{7}-\sqrt{5}}
$ simplifies to $
\sqrt{7}+\sqrt{5}
$.
