答：
x>1,x-1>0
y=(x^2-4x+9)/(x-1)
=[(x-1)^2-2(x-1)+10] / (x-1)
=(x-1)+10/(x-1) -2
>=2√[(x-1)*10/(x-1)]-2
=2√10 -2
当且仅当x-1=10/(x-1)即x-1=√10,x=1+√10时取得最小值2√10-2是+6不是+10吧哦，不好意思，重新解答如下：


答：
x>1，x-1>0
y=(x^2-4x+9)/(x-1)
=[(x-1)^2-2(x-1)+6] / (x-1)
=(x-1)+6/(x-1) -2
>=2√[(x-1)*6/(x-1)]-2
=2√6 -2
当且仅当x-1=6/(x-1)即x-1=√6，x=1+√6时取得最小值2√6-2