Question

How do you simplify `(4+sqrt2)/(3+2sqrt3)`?

Answer 1

I think you're asking for rationalizing?
Answer: `-12+11sqrt(2)-2sqrt(6)`

Explanation:

You rationalize it by multiply both numerator and denominator with its conjugate, which is: `3-sqrt(2)`

`(4+sqrt(2))/(3+sqrt(2)) ((3+sqrt(2))/(3+sqrt(2)))`
`=(12+3sqrt(2)-8sqrt(2)-2sqrt(2)sqrt(3))/(3^2-4(3)`
`=-(12-5sqrt(2)-2sqrt(6))/3`