Question

1/root 3+root 2-1
pls help

Answer 1

Answer in file attached.

Thank you;-)

Answer 2

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

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

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

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

$= \frac{ - 2 \sqrt{2} - 2 \sqrt{6} + 4 }{8} = \frac{2(2 - \sqrt{2} - \sqrt{6} ) }{8}$

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

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