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Rationalisation

Solve 3√ 5 ...

Question

Solve $\frac{3 \sqrt{5} - \sqrt{7}}{3 \sqrt{3} + \sqrt{2}}$

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Solution

$\frac{3 \sqrt{5} - \sqrt{7}}{3 \sqrt{3} + \sqrt{2}} = \frac{3 \sqrt{5} - \sqrt{7}}{3 \sqrt{3} + \sqrt{2}} \times \frac{3 \sqrt{3} - \sqrt{2}}{3 \sqrt{3} - \sqrt{2}} = \frac{(3 \sqrt{5} - \sqrt{7}) (3 \sqrt{3} - \sqrt{2})}{{(3 \sqrt{3})}^{2} - {(\sqrt{2})}^{2}} = \frac{9 \sqrt{15} - 3 \sqrt{10} - 3 \sqrt{21} + \sqrt{14}}{27 - 2} = \frac{9 \sqrt{15} - 3 \sqrt{10} - 3 \sqrt{21} + \sqrt{14}}{25}$

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