x-1/x = sqr 6 - 3 - 1/sqr 6 - 3
= (sqr6-3)^2 - 1 / sqr 6 - 3
= (6 +9 - 6 sqr6 - 1)/ sqr 6 - 3
= 14 - 6 sqr 6/ sqr 6 - 3
= 2(7-3sqr6)/sqr 6 - 3
taking conjugate,
2(7-3sqr6)/sqr6-3 * sqr 6 +3/ sqr6 +3
= 2( 7 sqr6 +21-18-9sqr6)/ 6 - 9
=2 ( -2 sqr6 +3)/-3
= -4sqr6 +3/ -3
= (4sqr 6 - 3)/ 3