Answer
$\dfrac{a+\sqrt{ab}+\sqrt{a}+\sqrt{b}}{4a-b}$
Work Step by Step
Rationalizing the denominator of $
\dfrac{\sqrt{a}+1}{2\sqrt{a}-\sqrt{b}}
$ results to
\begin{array}{l}
\dfrac{\sqrt{a}+1}{2\sqrt{a}-\sqrt{b}}
\cdot
\dfrac{\sqrt{a}+\sqrt{b}}{2\sqrt{a}+\sqrt{b}}
\\\\=
\dfrac{(\sqrt{a})(\sqrt{a})+(\sqrt{a})(\sqrt{b})+(1)(\sqrt{a})+(1)(\sqrt{b})}{(2\sqrt{a})^2-(\sqrt{b})^2}
\\\\=
\dfrac{(\sqrt{a})(\sqrt{a})+(\sqrt{a})(\sqrt{b})+(1)(\sqrt{a})+(1)(\sqrt{b})}{(2\sqrt{a})^2-(\sqrt{b})^2}
\\\\=
\dfrac{a+\sqrt{ab}+\sqrt{a}+\sqrt{b}}{4a-b}
.\end{array}