If I were to attempt polynomial division on this expression:
$\dfrac{a^2+ad+ac+cd-2ab-2bd}{a^2-ad-ac+cd} $,
I would get $(a^2-ad-ac+cd)(1)+2ad+2ac-2ab-2bd$.
Where $2ad+2ac-2ab-2bd$ is the remainder.
Thus $(a^2-ad-ac+cd)(1)+2ad+2ac-2ab-2bd=a^2+ad+ac+cd-2ab-2bd$.
But writing down $\dfrac{a^2+ad+ac+cd-2ab-2bd}{a^2-ad-ac+cd} =a^2+ad+ac+cd-2ab-2bd$ doesn't make sense. Where did I go wrong? Thanks.