y=[(x-2)(x-1)+1]/(x-2)
=(x-2)(x-1)/(x-2)+1/(x-2)
=x-1+1/(x-2)
=(x-2)+1/(x-2)+1
x>2
x-2>0
(x-2)+1/(x-2)+1>=2√[(x-2)*1/(x-2)]+1=2+1=3
所以最小值=3