Question

2√6-√5/3√5-2√6 rationalise the denominator and simplify​

Answer 1

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$\longrightarrow \: \: \bf \purple{{ \frac{2 \sqrt{6} + \sqrt{5} }{3 \sqrt{5} - 2 \sqrt{6} } }}$

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$= \rm{ \frac{2 \sqrt{6 } + \sqrt{5} }{3 \sqrt{5} - 2 \sqrt{6}} \times \frac{3 \sqrt{5} + 2 \sqrt{6} }{3 \sqrt{5} + 2 \sqrt{6} }(rationalisation\:of \:denominator ) }$

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$= \rm{ \frac{(2 \sqrt{6} + \sqrt{5})(3 \sqrt{5} + 2 \sqrt{6} ) }{9 \times 5 - 4 \times 6} }$

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$= \rm{ \frac{(2 \sqrt{6} \times 3 \sqrt{5} + 2 \sqrt{6} \times 2 \sqrt{6} + \sqrt{5} \times 3 \sqrt{5} + \sqrt{5} \times 2 \sqrt{6} )}{45 - 24} }$

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$= \rm{ \frac{(6 \sqrt{30} + 24 + 15 + 2 \sqrt{30}) }{21} }$

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$\red{ =} \bf \green{ \frac{39 + 8 \sqrt{3} }{21} }$