# 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.