Question

二次函数、方程、不等式的关系2解关于x的不等式a(x-1)/x-2＞1

Answer 1

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

(ax-a)/(x-2)-1>0

(ax-a-x+2)/(x-2)>0

所以(ax-a-x+2)(x-2)>0

[(a-1)x-(a-2)](x-2)>0

若a-1>0,a>1

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)