已知关于X的方程6/X-1=X+3/X(X-1)-K/X有解,求K?

两边乘x(x-1)
6x=x+3-k(x-1)=x+3-kx+k
(k+5)x=k+3
有解则k+5≠0
k≠-5
x=(k+3)/(k+5)
x≠0,x≠1
(k+3)/(k+5)≠0,k≠-3
(k+3)/(k+5)≠1,不成立
所以k≠-5且k≠-3