I have an objective function with a division involving a variable x.

If I solve it, it returns error due to division by zero.

If I add a lower bound, it halts and says infeasible solution.
Why would it do this? If I remove the term that involves division by zero, the problem becomes feasible (with a nonzero x), so clearly infeasibility is not the problem?
I managed to multiply through by x and get rid of the division, but is that really the only way? (It’s not possible every time either …)