Alg2.1.13

Rationalise $\frac{1}{2\sqrt{3}-3\sqrt{2}}\,$

Multiplying the numerator and denominator with

$2\sqrt{3}+3\sqrt{2}\,$

$\frac{2\sqrt{3}+3\sqrt{2}}{(2\sqrt{3}+3\sqrt{2})(2\sqrt{3}-3\sqrt{2})}\,$

Simplifying the denominator gives

$\frac{2\sqrt{3}+3\sqrt{2}}{(2\sqrt{3})^2-(3\sqrt{2})^2}\,$

$\frac{2\sqrt{3}+3\sqrt{2}}{12-18}\,$

$\frac{2\sqrt{3}+3\sqrt{2}}{-6}\,$

Simplifying we get

$\frac{-1}{\sqrt{3}}+\frac{-1}{\sqrt{2}}\,$