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Addition and Subtraction of Like and Unlike Surds

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Question

Solve : $\frac{4}{3 \sqrt{3} - 2 \sqrt{2}} + \frac{3}{3 \sqrt{3} + 2 \sqrt{2}}$

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Solution

$\frac{4}{3 \sqrt{3} - 2 \sqrt{2}} + \frac{3}{3 \sqrt{3} + 2 \sqrt{2}}$
Multiplying the denominators with their reciprocals we get,
$= \frac{4 (3 \sqrt{3} + 2 \sqrt{2}) + 3 (3 \sqrt{3} - 2 \sqrt{2})}{(3 \sqrt{3})^{2} - (2 \sqrt{2})^{2}} = \frac{21 \sqrt{3} + 2 \sqrt{2}}{19}$

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