Implicit hypothesis in the simplification of an equation

I have therefore tried to simplify an equation (see below).

(Laplace[V[r,[Theta][Phi]], {r, [Theta][Phi]}, "Spherical"]//Simplify)
% == 0
%//Simplify

What is strange is that when I had just the expression of the first line, the code was evaluated with r ^ 2 at the denominator. However, after defining this expression == 0 on the second line, then simplified on the third, the denominator has become r.

If Mathematica were to multiply both sides of the equation by r, why not simply eliminate the denominator completely by multiplying by r ^ 2?

PS. I am a beginner, so do not use anything too complex to explain.