Question

Rationalise 1/2+√3+2/√5-√3=-1/2-√5

Answer 1

Answer:

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

$= \frac{2 - \sqrt{3} }{(2 + \sqrt{3)(2 - \sqrt{3}) } } + \frac{2( \sqrt{5} + \sqrt{3} ) }{ (\sqrt{5} + \sqrt{3)}( \sqrt{5 - \sqrt{3}) } }$

$= \frac{2 - \sqrt{3} }{4 - 3} + \frac{2( \sqrt{5} + \sqrt{3} ) } { 5 - 3 }$

$= 2 - \sqrt{3} + \sqrt{5} + \sqrt{3}$

$= 2 + \sqrt{5}$

$= \frac{1}{(2 + \sqrt{5} )}$

Hence proved

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