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)