Question

Rationalise the denominator and simplify 2√6-√5 /3√5-2√6

Answer 1

Answer:

$\frac{2\sqrt{6}-\sqrt{5}}{3\sqrt{5}-2\sqrt{6}}=\frac{4\sqrt{30}+9}{21}$

Step-by-step explanation:

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

$=\frac{2\sqrt{6}-\sqrt{5}}{3\sqrt{5}-2\sqrt{6}}\times \frac{3\sqrt{5}+2\sqrt{6}}{3\sqrt{5}+2\sqrt{6}}$

$=\frac{2\sqrt{6}(3\sqrt{5}+2\sqrt{6})-\sqrt{5}(3\sqrt{5}+2\sqrt{6})}{(3\sqrt{5})^{2}-(2\sqrt{6})^{2}}$

$=\frac{6\sqrt{30}+24-15-2\sqrt{30}}{45-24}$

$=\frac{4\sqrt{30}+9}{21}$

Therefore,

$\frac{2\sqrt{6}-\sqrt{5}}{3\sqrt{5}-2\sqrt{6}}=\frac{4\sqrt{30}+9}{21}$

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Answer 2

Answer:

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Step-by-step explanation:

Answer:

\frac{2\sqrt{6}-\sqrt{5}}{3\sqrt{5}-2\sqrt{6}}=\frac{4\sqrt{30}+9}{21}

Step-by-step explanation:

Given\: \frac{2\sqrt{6}-\sqrt{5}}{3\sqrt{5}-2\sqrt{6}}

=\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{2\sqrt{6}(3\sqrt{5}+2\sqrt{6})-\sqrt{5}(3\sqrt{5}+2\sqrt{6})}{(3\sqrt{5})^{2}-(2\sqrt{6})^{2}}

=\frac{6\sqrt{30}+24-15-2\sqrt{30}}{45-24}

=\frac{4\sqrt{30}+9}{21}

Therefore,

\frac{2\sqrt{6}-\sqrt{5}}{3\sqrt{5}-2\sqrt{6}}=\frac{4\sqrt{30}+9}{21}

plz mark me as brainliest...