Okay, hopefully enough time has gone by so that if this was an assignment it is already due (either that or enough time has passed so that you've found the answer on your own).
So why is it that 0 divided by 0 cannot be defined?
Well, say that 0 divided by 0 were defined to be some number, call it k.
Given that all other numbers x not equal to zero have x/x = 1 it would seem that k must also equal 1.
However note that following the rules for addition of fractions we would also have 2k = k since zero over zero plus zero over zero has a common denominator and zero plus zero equals zero. But if 2k = k then we get that 2k - k = 0 or k = 0.
Since we cannot have k both equal to 1 and equal to 0 we are forced to leave zero over zero an undefined quanity.
Perhaps not the most convincing way of arguing this, but it should convey the idea...
Any other comments?
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