Calculus only provides a mechanism for dividing by almost zero, to the extent that almost zero is so close to zero that it doesn't matter.

Dividing by zero gives meaningless answers, for example:
(x^2 means x squared where x is an arbitrary variable)

x = 1 {initial statement}
x^2 = x {multiply by x}
x^2 - 1 = x - 1 {subtract 1}
(x+1)*(x-1) = x - 1 {factorise left}
x + 1 = 1 {divide (x-1)}
1 + 1 = 1 {because x = 1 (see line 1)}
2 = 1


This contains a divide by zero because (x-1) = 0. This shows by contradiction that dividing by zero is not a valid operation.