Rate = Distance/Time
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That is correct.
A zero. Zero in the denominator make the expression undefined for algebraic purposes.
When the denominator is equal to zero, the expression is undefined. Close to those places, the expression tends towards plus infinity, or minus infinity. In other words, setting the denominator to zero will tell you where there are vertical asymptotes.
You could write "divided by" between the expression for the numerator and the expression for the denominator.
The value of the denominator cannot be zero.