Question: Rationalize the denominators and simplify: $\dfrac{5}{3\sqrt{7} + 2\sqrt{3}}$

Solution:
Given,

$= \dfrac{5}{3\sqrt{7} + 2\sqrt{3}}$

$= \dfrac{5}{3\sqrt{7} + 2\sqrt{3}} × \dfrac{3\sqrt{7} - 2\sqrt{3}}{3\sqrt{7} - 2\sqrt{3}}$

$= \dfrac{5(3\sqrt{7} - 2\sqrt{3})}{(3\sqrt{7})^2 - (2\sqrt{3})^2}$

$= \dfrac{5(3\sqrt{7} - 2\sqrt{3})}{63-12}$

$= \dfrac{5(3\sqrt{7} - 2\sqrt{3})}{51}$

$= \dfrac{5}{51} (3\sqrt{7} - 2\sqrt{3})$
= Answer