To simplify the given expression \(\frac{2\sqrt{3} + 3\sqrt{5}}{3\sqrt{5} - 2\sqrt{3}}\), we'll rationalize the denominator by multiplying both the numerator and denominator by the conjugate of the denominator, which is \(3\sqrt{5} + 2\sqrt{3}\):

\(

\begin{align}

\frac{2\sqrt{3} + 3\sqrt{5}}{3\sqrt{5} - 2\sqrt{3}} &= \frac{(2\sqrt{3} + 3\sqrt{5})(3\sqrt{5} + 2\sqrt{3})}{(3\sqrt{5} - 2\sqrt{3})(3\sqrt{5} + 2\sqrt{3})} \\

&= \frac{(2\sqrt{3})(3\sqrt{5}) + (3\sqrt{5})(3\sqrt{5}) + (2\sqrt{3})(2\sqrt{3}) + (3\sqrt{5})(2\sqrt{3})}{(3\sqrt{5})(3\sqrt{5}) - (2\sqrt{3})(2\sqrt{3})} \\

&= \frac{6\sqrt{15} + 45 + 12 + 6\sqrt{15}}{45 - 12} \\

&= \frac{18\sqrt{15} + 57}{33} \\

&= \frac{3(6\sqrt{15} + 19)}{33} \\

&= \frac{6\sqrt{15} + 19}{11}

\end{align}

\(

The simplified form of the expression is \(\frac{6\sqrt{15} + 19}{11}\).