Answer
$\dfrac{\sqrt{35}-\sqrt{14}+5-\sqrt{10}}{3}$
Work Step by Step
Factoring the $-1$ from the numerator, the given expression, $
\dfrac{\sqrt{7}+\sqrt{5}}{\sqrt{5}+\sqrt{2}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{\sqrt{7}+\sqrt{5}}{\sqrt{5}+\sqrt{2}}\cdot\dfrac{\sqrt{5}-\sqrt{2}}{\sqrt{5}-\sqrt{2}}
\\\\=
\dfrac{\sqrt{7}(\sqrt{5})+\sqrt{7}(-\sqrt{2})+\sqrt{5}(\sqrt{5})+\sqrt{5}(-\sqrt{2})}{(\sqrt{5})^2-(\sqrt{2})^2}
\\\\=
\dfrac{\sqrt{7(5)}-\sqrt{7(2)}+\sqrt{5(5)}-\sqrt{5(2)}}{5-2}
\\\\=
\dfrac{\sqrt{35}-\sqrt{14}+\sqrt{(5)^2}-\sqrt{10}}{3}
\\\\=
\dfrac{\sqrt{35}-\sqrt{14}+5-\sqrt{10}}{3}
.\end{array}
