I got different answer then you.
First i multiplied 2√2 / √3-1 by √3+1 / √3+1 and simplified to get √6 +√2
and then i multiplied 2√3 / √2 +1 by √2-1 / √2-1 and simplified to get 2√6 -2√3
then did (√6 +√2) - (2√6 -2√3)
and i got -√6 + 2√3 +√2
so P = -1 Q = 2 R = 1
(I am not entirely sure of my answers)