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

Question

1602 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-10-02T12:51:00

$sqrt11-4$

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

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

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

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

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