[a(x-1)/(x-2)]-1>0求x的范围.

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[a(x-1)/(x-2)]-1>0求x的范围.[a(x-1)/(x-2)]-1>0求x的范围.[a(x-1)/(x-2)]-1>0求x的范围.[a(x-1)/(x-2)]-1>0(ax-a-x+2)

[a(x-1)/(x-2)]-1>0求x的范围.
[a(x-1)/(x-2)]-1>0求x的范围.

[a(x-1)/(x-2)]-1>0求x的范围.
[a(x-1)/(x-2)]-1>0
(ax-a-x+2)/(x-2)>0
[(a-1)x-(a-2)]/(x-2)>0
(1)
当a-1>0,即a>1时
x1=(a-2)/(a-1)=1-[1/(a-1)<1<2,x2=2
于是解为x>2或x<(a-2)/(a-1)
(2)
当a-1=0,即a=1时
原不等式为1/(x-2)>0,
解为x>2
(3)
当a-1<0,即a<1时
[(a-1)x-(a-2)]/(x-2)>0
[(1-a)x+(a-2)]/(x-2)<0
x1=(a-2)/(a-1),x2=2
①当x1>x2,即0<a<1时
解为2<x<(a-2)/(a-1)
②当x1=x2,即a=0时
原不等式无解
③当x1<x2,即a<0时
解为(a-2)/(a-1)<x<2

X>(a-2)/(a-1)