解不等式（ax-a)/(x-2)>1(a≠1)

(ax-a)/(x-2)-1>0
(ax-a-x+2)/(x-2)>0
两边乘(x-2)^2>0
所以[(a-1)x-(a-2)](x-2)>0

若a>1,a-1>0
两边除a-1
[x-(a-2)/(a-1)](x-2)>0
(a-2)/(a-1)=(a-1-1)/(a-1)=1-1/(a-1)
因为a-1>0,所以-1/(a-1)<0
1-1/(a-1)<1<2
所以x>2,x<(a-2)/(a-1)

若0<a<1,-1<a-1<0
两边除a-1
[x-(a-2)/(a-1)](x-2)<0
(a-2)/(a-1)=(a-1-1)/(a-1)=1-1/(a-1)
因为-1<a-1<0,所以-1/(a-1)>1
1-1/(a-1)>2
所以2<x<(a-2)/(a-1)

若a=0
则(x-2)^2<0
无解

若a<0,则a-1<-1
两边除a-1
[x-(a-2)/(a-1)](x-2)<0
(a-2)/(a-1)=1-1/(a-1)
因为a-1<-1,所以
1<1/(a-1)<0
0<-1/(a-1)<1
1<1-1/(a-1)<2
所以(a-2)/(a-1)<x<2