Avoiding dividing by 0 in an equation

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Crusty
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What was the method for modifying an equation to avoid dividing by zero?
I think it involved adding 1 somewhere, then removing the error that creates later.


For example,

a / b = c

It is possible that one of the values placed in the b variable could be 0. How would the equation be modified so that dividing by zero wouldn't occur?
 
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Its a commonly left out detail, sometimes considered obvious, sometimes completely forgotten. When you have a fraction a/b, b can not equal zero. Its a restriction placed on b in order for the division to be defined.
 
Of course there's the possibility that in the limit a->0 and b->0 ; a/b equals a real number and the eqn. makes sense. Hard to tell without context.