Okay, not sure which one you're asking for proof for, but, seems a worthwhile proof to give =p
Let x/0 = a
From this, x = 0*a
This is false for all x EXCEPT x = 0.
Let's approach 0/0 then. 0/0 = 0? Okay, then 0*0=0, that works, no problem, right?
Well, 0/0 = 1, 0*1 = 0, no...