解关于x的不等式a(x-1)/(x-2)>1(a不等于1)

Question

解关于x的不等式a(x-1)/(x-2)>1(a不等于1)

Answer 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若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-11
1-1/(a-1)>2
所以2若a=0
则(x-2)^2<0
无解
若a<0,则a-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-11<1/(a-1)<0
01<1-1/(a-1)<2
所以(a-2)/(a-1)

作业帮用户 2017-10-31