Answer
$\frac{15+26\sqrt{x}+8x}{9-16x}$
Work Step by Step
Given \begin{equation}
\frac{5+2 \sqrt{x}}{3-4 \sqrt{x}}.
\end{equation} Simplify by rationalizing the denominator.
\begin{equation}
\begin{aligned}
\frac{5+2 \sqrt{x}}{3-4 \sqrt{x}}&=\frac{(5+2 \sqrt{x})}{(3-4 \sqrt{x})}\cdot \frac{\left(3+4 \sqrt{x}\right) }{\left( 3+4\sqrt{x}\right) }\\
& =\frac{5(3+4 \sqrt{x})+2\sqrt{x}(3+4 \sqrt{x})}{9-16x}\\
&=\frac{15+20\sqrt{x}+6\sqrt{x}+8x}{9-16x}\\
&=\frac{15+26\sqrt{x}+8x}{9-16x}.
\end{aligned}
\end{equation}
