Answer
$\dfrac{a+7\sqrt{a}+10}{a-25}$
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{\sqrt{a}+2}{\sqrt{a}-5}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{\sqrt{a}+2}{\sqrt{a}-5}\cdot\dfrac{\sqrt{a}+5}{\sqrt{a}+5}
\\\\=
\dfrac{\sqrt{a}(\sqrt{a})+\sqrt{a}(5)+2(\sqrt{a})+2(5)}{(\sqrt{a})^2-(5)^2}
\\\\=
\dfrac{a+5\sqrt{a}+2\sqrt{a}+10}{a-25}
\\\\=
\dfrac{a+7\sqrt{a}+10}{a-25}
.\end{array}
