The reason that the result of a division by zero is undefined is that any attempt at a definition leads to contradiction
for instance:
r X 0 = a
but r X 0 = 0
for all numbers r, and so unless a = 0 there is no solution of the equation.
Also, the reason why is impossible to divide by zero mathematically, is that zero has no multiplicative inverse, and any attempt to define a real number as the multiplicative inverse of zero would result in contradiction 0 = 1. recall mathematics starts by assuming there are objects called real numbers
Dividing by zero doesn't make sense because in mathematics, dividing by zero can also be interpreted as multiplying by zero.
For example:
if 3/0 = x, its same equation as 0 X x = 3. Obviously, there is no number that can be plugged in for x to make the equation work. And x can be anything so, the equation is not very useful