\(\begin{array}{l}
\quad \dfrac{\left(2 + \sqrt3\right)^2 - 1}{\left(\sqrt3 + 1\right)^2}:\dfrac{\left(3 + \sqrt5\right)^2 - 4}{\left(\sqrt5 + 1\right)^2}\\
= \dfrac{\left(1 + \sqrt3\right)\left(3 + \sqrt3\right)}{\left(\sqrt3 + 1\right)^2}:\dfrac{\left(1 + \sqrt5\right)\left(5 + \sqrt5\right)}{\left(\sqrt5 + 1\right)^2}\\
= \dfrac{\sqrt3\left(1 + \sqrt3\right)^2}{\left(\sqrt3 + 1\right)^2}\cdot\dfrac{\left(\sqrt5 + 1\right)^2}{\sqrt5\left(1 + \sqrt5\right)^2}\\
=\dfrac{\sqrt3}{\sqrt5}\\
= \dfrac{\sqrt{15}}{5}
\end{array}\)
