Question

How do you rationalize `(sqrt3-1) /(sqrt3+1)`?

Answer 1

Multiply and divide by `sqrt(3)-1` and get:
`(sqrt(3)-1)/(sqrt(3)+1)*(sqrt(3)-1)/(sqrt(3)-1)=(sqrt(3)-1)^2/(3-1)=(sqrt(3)-1)^2/2=(3-2sqrt(3)+1)/2=(4-2sqrt(3))/2=2(2-sqrt(3))/2=2-sqrt(3)`

Answer 2

`(sqr3 - 1)/(sqr3 + 1). (sqr3 - 1)/(sqr3 - 1)`= `(sqr3 - 1)^2/2`