(a²-b²+2)/2-(a²-2b²+1)/3
=[(3a²-3b²+6)-(2a²-4b²+2)]/6
=(a²+b²+4)/6
∵a²+b²≥0
∴(a²+b²+4)/6>0
∴(a²-b²+2)/2>(a²-2b²+1)/3