Question

$5 + \sqrt{6} \div 5 - \sqrt{6}$
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Answer 1

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According to question:-

$= \frac{5 + \sqrt{6} }{5 - \sqrt{6} }$

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

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

$= \frac{ {5}^{2} + {( \sqrt{6} })^{2} + 2(5)( \sqrt{6} )}{25 - 6}$

$= \frac{25 + 6 + 10 \sqrt{6} }{19}$

$= \frac{31 + 10 \sqrt{6} }{19}$

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