解关于X的不等式:a(X-1)/X-2>1(a
1个回答

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

a(x-1)(x+2) > (x+2)^2

ax^2+ax-2a > x^2+4x+4

(a-1)x^2+(a-4)x-(2a+4) > 0

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

∵a < 1

∴a-1 < 0

当(a+2)/(a-1)=-2时

a+2=-2a+2

3a=0

a=0

∴当a=0时

(-x-2)(x+2) > 0

(x+2)^2 < 0

∴x无解

当1 > a > 0时

(a+2)/(a-1) < -2

∴(a+2)/(a-1) < x < -2

当a < 0时

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

∴-2 < x < (a+2)/(a-1)