y=(x²+8)/(x-1)
=[(x-1)²+2(x-1)+9]/(x-1)
=(x-1)+9/(x-1)+2
x>1所以x-1>0
所以(x-1)+9/(x-1)>=2√(x-1)*[9/(x-1)]=6
所以y>=6+2=8
所以y最小值为8