Yes, the answer is that the result of x/0 (including x=0) is every possible result at once. That is because x*0 is zero for any x. With x*a for any a != 0 the result set is exactly as large as the definition set (I hope these are the correct English terms). But for a = 0, the result set has only a single value, 0 itself.

x*a maps every x to one distinct y, except for a=0, so you can reverse it. But for a=0, it maps every x to the same y (that is, to 0), so by knowing a=0 and y=0 you still cannot tell which out of an infinite number of possible values for x led to this result.

Makeshifts last the longest.