If p, q are rational numbers and $p - \sqrt{15}q = \dfrac{2\sqrt{3} - \sqrt{5}}{4\sqrt{3} - 3\sqrt{5}}$, find the values of p and q.

Since, it is given that

$\dfrac{2\sqrt{3} - \sqrt{5}}{4\sqrt{3} - 3\sqrt{5}} = p - \sqrt{15} q$

On solving,

$\dfrac{2\sqrt{3} - \sqrt{5}}{4\sqrt{3} - 3\sqrt{5}} × \dfrac{4\sqrt{3} + 3\sqrt{5}}{4\sqrt{3} + 3\sqrt{5}} \\[1.5em] = \dfrac{2\sqrt{3} × 4\sqrt{3}+ 2\sqrt{3} × 3\sqrt{5} - \sqrt{5} × 4\sqrt{3} - \sqrt{5} × 3\sqrt{5} }{(4\sqrt{3})^2 -(3\sqrt{5})^2} \\[1.5em] = \dfrac{24 + 6\sqrt{15} - 4\sqrt{15} - 15 }{(4\sqrt{3})^2 -(3\sqrt{5})^2} \\[1.5em] = \dfrac{24 - 15 + 6\sqrt{15} - 4\sqrt{15} }{48 - 45} \\[1.5em] = \dfrac{9 + 2{\sqrt{15}}}{3} \\[1.5em] = \dfrac{9}{3} + \dfrac{2\sqrt{15}}{3} \\[1.5em] = 3 + \dfrac{2}{3}{\sqrt{15}} \\[1.5em] \therefore 3 - \Big(-\dfrac{2}{3}\Big){\sqrt{15}} = p - q\sqrt{15}$

Hence, p = 3 and q = $-\dfrac{2}{3}$.