If $q$ and $r$ are quaternions, and $p$ is a point, applying $q$ then $r$ to $p$ is:
$$ (qr)p\dfrac{1}{qr} $$
What if I want to go the other way? Instead of concatenating rotations, I want to remove them.
So, I have $q$ and $m$, and I know that $qx =m$, but I don't know what $x$ is. How can I discover $x$? (How can I do quaternion divison?)