The Art of Dividing by Zero is... CALCULUS! For example; to find a slope of a line, use this simple formula:
m = (y2-y1)/(x2-x1)
Where:
m = the slope,
(x1,y1) = coordinate for first point, and
(x2,y2) = coordinate for second point.
Easy. Now, how do you find the slope of a line that rests tangent on a curve? Well, you can pick two points on that curve at either side of the tangent point and use the SLOPE EQUATION to get a good approximation. To get a more accurate answer, move these two points closer to the tangent point and use the equation again. To get the EXACT answer, move those two points DIRECTLY on the target point itself. Unfortunately...
Because:
y2=y1, and
x2=x1, then
m = 0/0
Yikes! Not only are you dividing by ZERO, but you are dividing ZERO by ZERO. Call it a nightmare, a devastating tragedy, or even ask yourself; "Is there NO GOD???"
But yet, amid the confusion there IS an answer. Inside that tiny point, an entire universe of mathematics called CALCULUS is unveiled. From Derivatives to Integrals to Differential Equations, there are many ways to unlock the secret of dividing by zero. Many books have been written on the subject that teach this mysterious art.