Dividing one equation by another (may one is zero?!) there's something confusing me about how do we divide two equation by each other? but may one is zero .. no?!

lets assume I have like this:
(1) x=y
(2)z=m
how do we do (x/z)=(y/m) without caring about if z is zero or m is zero .. then we can't do division .. so how we do division ?! thanks a lot.

if z or m is zero then we can't do division .. so how we say that we can division two equation one by another?
As you state, if $z = m = 0$ the division makes no sense. You'd have to add that restriction and handle the case $m = 0$ separately.

Without further details, we can't say anything more.
You can write $$\begin{cases}x=y,\\z=m\end{cases}\iff \begin{cases}x=y,\\z=m=0\end{cases}\lor \begin{cases}x=y,\\\dfrac xz=\dfrac ym\end{cases}.$$