Question

please solve it as soon as possible​

Answer 1

these are your answers dear

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Answer 2

Step-by-step explanation:

(1)

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

$= \frac{1 - \sqrt{2} - \sqrt{3} }{1 - (2 + 3 + 2 \sqrt{6}) }$

(simplifying the denominator)

$= \frac{1 - \sqrt{2} - 3 }{2 \sqrt{6} - 4 } = \frac{(1 - \sqrt{2} - \sqrt{3})(2 \sqrt{6} + 4) }{(2 \sqrt{6 }+ 4 )(2 \sqrt{6} - 4) }$

$\frac{2 \sqrt{6} - 2 \sqrt{12} - 2 \sqrt{18} + 4 - 4 \sqrt{2} - 4 \sqrt{3} }{20}$

$= \frac{ \sqrt{6} - \sqrt{12} - \sqrt{18} + 2 - 2 \sqrt{2} - 2 \sqrt{3} } {10}$

(2)

$\frac{1}{ \sqrt{2} + \sqrt{3} + \sqrt{5} } = \frac{ \sqrt{2} - \sqrt{3} - \sqrt{5} }{2 \sqrt{15} - 6 }$

$\frac{1}{ \sqrt{2} + \sqrt{3} + \sqrt{5} } = \frac{ \sqrt{2} - \sqrt{3} - \sqrt{5} }{2 \sqrt{15} - 6 } = \frac{ (\sqrt{2} - \sqrt{3} - \sqrt{5})(2 \sqrt{15} + 6)}{54}$

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