Question

How do you simplify `(3 - 2sqrt11)/(2+sqrt11)`?

Answer 1

`sqrt11-4`

Explanation:

`(3-2sqrt(11))/(2+sqrt(11))=(3-2sqrt(11))/(2+sqrt(11))*(2-sqrt11)/(2-sqrt11)=`

`=(3*2-3*sqrt11-2*2sqrt11+2sqrt11sqrt11)/(2*2-2*sqrt11+2*sqrt11-sqrt11*sqrt11)=`

`=(6-3sqrt11-4sqrt11+2*11)/(4-2sqrt11+2sqrt11-11)=(28-7sqrt11)/(-7)=`

`=(-7(-4+sqrt11))/(-7)=sqrt11-4`