Consider Laplace's equation in spherical coordinates $$\nabla^2 f = \frac{1}{r^2}\frac{\partial }{\partial r}\left(r^2 \frac{\partial f}{\partial r}\right)+\frac{1}{r^2\sin\theta}\frac{\partial}{\partial \theta}\left(\sin\theta\frac{\partial f}{\partial\theta}\right) + \frac{1}{r^2\sin^2\theta}\frac{\partial^2f}{\partial \psi^2}=0$$
Removing the $1/{r^2}$ factor on the LHS would still make the equation true, so why is it retained?