When proving a certain value is the limit using the ϵ-N convergence definition for sequences

Why can't you just remove a term by its self

ie (this is meant to be a very simplistic example), but why can't you just go x/(x^2+x-1) < x/(x^2-1), since this is for a sequence so it's assumed that x>0? Why is it that you can only remove constants? Thank you