# Condition of existence while solving inequalities

I would like to have solutions of inequalities where condition of existence are included, but Reduce doesn't work like this, it would simplify the denominators before solving, like this:

Reduce[(x^2 + x)/x >= 0, Reals]
(* x >= -1 *)


Is there a way to have the solution with condition of existence of the original expression?

• Reduce[Exists[x, (x^2 + x)/x >= 0], Reals] gives True. Is this what you need? – Roman Mar 3 at 14:56

Simplify[

• @MarcoDisce That's because x/x will immediately evaluate to 1. You could use FunctionDomain[Hold[x/x], x] instead, which prevents evaluation. – MarcoB Mar 4 at 14:02