(3x+1)/(x+1)=k-2
3x+1=(x+1)(k-2)
3x+1=xk-2x+k-2
5x-xk=k-3
x(5-k)=k-3
x=(k-3)/(5-k)
(k-3)/(5-k)<0
(k-3)(5-k)<0
-(k-3)(k-5)<0
k∈(-∞,3)u(5,∞)
(3x+1)/(x+1)=k-2
3x+1=(x+1)(k-2)
3x+1=xk-2x+k-2
5x-xk=k-3
x(5-k)=k-3
x=(k-3)/(5-k)
(k-3)/(5-k)<0
(k-3)(5-k)<0
-(k-3)(k-5)<0
k∈(-∞,3)u(5,∞)