Question

1 + root 2/ 2- root 3?

Answer 1

I assume you want to rationalize the denominator. You start with

(1+√2)/(2-√3)
just multiply top and bottom by the conjugate of 2-√3, which is 2+√3
Now you have
(1+√2)(2+√3) / (2-√3)(2+√3) = (1*2 + 2√2 + 1*√3 + √6)/(2^2 - √3^2)
= (2 + 2√2 + √3 + √6)/(4-3)
= 2 + 2√2 + √3 + √6