Question

simplify [1/root3+root2] + [1/root2+1]

Answer 1

Answer:

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Answer 2

We have,

$\quad \: \frac{1}{ \sqrt{3} + \sqrt{2} } + \frac{1}{ \sqrt{2} + 1} \\ \\ = \frac{1( \sqrt{3} - \sqrt{2} )}{( \sqrt{3} + \sqrt{2} )( \sqrt{3} - \sqrt{2} )} + \frac{1( \sqrt{2} - 1)}{( \sqrt{2} + 1)( \sqrt{2} - 1)} \sf ---------[Rationalising] \\ \\ = \frac{ \sqrt{3} - \sqrt{2} }{( { \sqrt{3} )}^{2} - {( \sqrt{2} )}^{2} } + \frac{ \sqrt{2} - 1 }{ {( \sqrt{2} )}^{2} - {(1)}^{2} } --------[ \because ( {a}^{2} - {b}^{2} ) = (a-b)(a+b) ]\\ \\ = \frac{ \sqrt{3} - \sqrt{2} }{3 - 2} + \frac{ \sqrt{2} - 1}{2 - 1} \\ \\ = \frac{ \sqrt{3} - \sqrt{2} }{1} + \frac{ \sqrt{2} - 1}{1} \\ \\ = \sqrt{3} - \cancel{\sqrt{2} } + \cancel{ \sqrt{2} } - 1 \\ \\ \bf = \quad \sqrt{3} - 1$

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