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