Question

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

Answer 1

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

Answer 2

http://znanija.com/task/21360804

Answer 3

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