Simplify the following by rationalizing the denominator.
$\frac{1}{3 \sqrt{2} - 2 \sqrt{3}}$

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Solution

Given $\frac{1}{3 \sqrt{2} - 2 \sqrt{3}}$
$= \frac{1}{3 \sqrt{2} - 2 \sqrt{3}} \times \frac{3 \sqrt{2} + 2 \sqrt{3}}{3 \sqrt{2} + 2 \sqrt{3}}$
$= \frac{3 \sqrt{2} + 2 \sqrt{3}}{(3 \sqrt{2})^{2} - (2 \sqrt{3})^{2}}$
$= \frac{3 \sqrt{2} + 2 \sqrt{3}}{18 - 12}$
$= \frac{3 \sqrt{2} + 2 \sqrt{3}}{6}$

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