Dividing by zero

[Simsim]

Most of what can be said has already been said. But I would like to add another thing.

There are cases when a denominator approaches zero but the total fraction doesn't approach infinity. This when the numerator can be algebraically analyzed into two parts one of them corresponds to the denominator.

Example:

(x^2 + x) / x , when x approaches zero the total fraction doesn't go to infinity. Because you can put the fraction in the following formula:

x*(x+1)/ x

By omitting x in the numerator with the x in the denominator the final result will be x+1 . Thus, when x approaches zero the polynomial (x+1) approaches 1 not infinity. Consequently, the fraction (x^2+x)/ x approaches 1 also when x approaches zero.