k/(a- 1/x)+(b- 1/x)/(c- 1/x)& lt； 0

Let y =-1/x.

Then the inequality we want to solve becomes:

k/(y+a)+(y+b)/(y+c)& lt； 0

And the title means y∈(-2,-1) ∩ (2,3).

So the solution of X can get X ∈ (1/2, 1)∨(- 1/2,-1/3).