Question

rationalise the denominator
please explain your answer​

Answer 1

Answer:

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

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

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

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

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

Answer 2

Answer:

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