Answer
$15+5\sqrt{7}$
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{10}{3-\sqrt{7}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{10}{3-\sqrt{7}}\cdot\dfrac{3+\sqrt{7}}{3+\sqrt{7}}
\\\\=
\dfrac{10(3+\sqrt{7})}{(3)^2-(\sqrt{7})^2}
\\\\=
\dfrac{10(3+\sqrt{7})}{9-7}
\\\\=
\dfrac{10(3+\sqrt{7})}{2}
\\\\=
\dfrac{\cancel{2}(5)(3+\sqrt{7})}{\cancel{2}}
\\\\=
5(3+\sqrt{7})
\\\\=
15+5\sqrt{7}
.\end{array}
