Here is the explanation I got that made a lot of sense to me: if we say 30/5 = 6, how do we check? We multiply both sides by 5: 30 = 5*6=30. True. Now let’s try with dividing by zero: 30/0 = a. No matter what value we pick for a, when we multiply we always get 30=0. That can never be true.
The only exception is 0/0. In this case, we could pick *any* value for a in the equation 0/0=a. When we multiply both sides, we always get 0=0, which is why this form is called indeterminate: it can be any value, we can’t determine which
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