原方程为:
(3-2x)/(x-3) - (2+mx)/(x-3) + (x-3)/(x-3) = 0
(3-2x-2-mx+x-3)/(x-3) = 0
[(-m-1)x-2]/(x-3) = 0
讨论:
(1)
当该式分子为不等于零的常数时,原方程无解,即:
-m-1=0
m=-1
(2)
当分子是分母的非零常数项倍数时,原方程无解,设此常数项为C(C≠0),即:
[(-m-1)x-2]/(x-3) = C
则:
(-m-1)[x-2/(-m-1)] = C(x-3)
2/(-m-1) = 3
m=-5/3
综上:m = -1 或者 -5/3 时,原方程无解