y=(x²-1+2)/(x-1)
=(x²-1)+2/(x-1)
=x+1+2/(x-1)
=(x-1)+2/(x-1)+2
x>1.x-1>0
所以(x-1)+2/(x-1)+2≥2√[(x-1)*2/(x-1)]+2=2√2+2
所以最小值=2√2+2