(1+√2+√3)/(1-√2+√3)=? Simplify

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Answer 1 · 2018-04-17T14:07:43

#(1+√2+√3)/(1-√2+√3)=sqrt3+sqrt2#

Let,
#X=(1+√2+√3)/(1-√2+√3)#

#=((1+sqrt3)+sqrt2)/((1+sqrt3)- sqrt2)xx((1+sqrt3)+sqrt2)/((1+sqrt3)+sqrt2)#

#=((1+sqrt3+sqrt2)^2)/((1+sqrt3)^2-(sqrt2)^2)#

#=(1+3+2+2sqrt3+2sqrt2+2sqrt6)/(1+2sqrt3+3-2)#

#=(6+2sqrt3+2sqrt2+2sqrt6)/(2+2sqrt3#

#=(3+sqrt3+sqrt2+sqrt6)/(1+sqrt3)#

#=[sqrt3(sqrt3+1)+sqrt2(1+sqrt3)]/(1+sqrt3)#

#=(cancel((1+sqrt3))(sqrt3+sqrt2))/(cancel((1+sqrt3))#

#=sqrt3+sqrt2#

Note:

If your question is #(1+sqrt(2+sqrt3))/(1-sqrt(2+sqrt3)# ,then

#X=(1+sqrt(2+sqrt3))/(1- sqrt(2+sqrt3))xx(1+sqrt(2+sqrt3))/(1+sqrt(2+sqrt3)#

and so on....