Question

Rationalise
$\frac{2 \sqrt{6 } - \sqrt{5} }{3 \sqrt{5} - 2 \sqrt{6 } }$

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Answer 1

$\frac{2 \sqrt{6} - \sqrt{5} }{3 \sqrt{5} - 2 \sqrt{6} } \times \frac{3 \sqrt{5} + 2 \sqrt{6} }{3 \sqrt{5} + 2 \sqrt{6} } \\ \\ = > \frac{6 \sqrt{30} + 24 - 15 - 2 \sqrt{30} }{45 - 24} \\ \\ = > \frac{4 \sqrt{30} + 9}{21}$

Answer 2

$\frac{2 \sqrt{6} - \sqrt{5} }{3 \sqrt{5} - 2 \sqrt{6} }$

2√6-√5*3√5+2√6/3√5-2√6*3√5+2√6

6√30-3√25+4√36-2√30/(3√5)²-(2√6)²

6√30-3*5+4*6-2√30/9*5-4*6

6√30-2√30-15+24/45-24

4√30+9/21

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