In this formula, a vacuous quantification can be removed:

$ \exists x \forall x (P(x) \rightarrow Q(x)) \equiv \forall x (P(x) \rightarrow Q(x)) $

What about a formula like this?:

$ \forall x (P(x) \rightarrow \exists x Q(x)) $

Is this also a vacuous quantification or is it not a well formed formula?

Can it be rewritten in a different form like for the first formula?