Question

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Answer 1

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

$\frac{1}{1 + \sqrt{2} + \sqrt{3} }$

$= \frac{1 \times (1 + \sqrt{2} - \sqrt{3} )}{(1 + \sqrt{2} + \sqrt{3})(1 + \sqrt{2} - \sqrt{3} ) }$

$= \frac{1 + \sqrt{2} - \sqrt{3} }{ {(1 + \sqrt{2} ) }^{2} - {( \sqrt{3} )}^{2} }$

$= \frac{1 + \sqrt{2} - \sqrt{3} }{1 + 2 \sqrt{2} + 2 - 3}$

$= \frac{1 + \sqrt{2} - \sqrt{3} }{2 \sqrt{2} }$

$= \frac{(1 + \sqrt{2} - \sqrt{3} ) \sqrt{2} }{2 \sqrt{2} \times \sqrt{2} }$

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

$= \frac{2 + \sqrt{2} - \sqrt{6} }{4}$

Ans.