Question

Rationalize the denominator: $\frac{1}{2\sqrt{7}+3\sqrt{3}}$

Answer 1

$\frac{1}{2\sqrt{7}+3\sqrt{3}}$
$=\frac{1}{2\sqrt{7}+3\sqrt{3}}\times \frac{2\sqrt{7}-3\sqrt{3}}{2\sqrt{7}-3\sqrt{3}}$
$=\frac{2\sqrt{7}-3\sqrt{3}}{{\left(2\sqrt{7}\right)}^2-{\left(3\sqrt{3}\right)}^2}$
$=\frac{2\sqrt{7}-3\sqrt{3}}{28-27}$
$=2\sqrt{7}-3\sqrt{3}$