Dividing by zero is meaningless, because in arithmetic, dividing by zero can also be interpreted as multiplying by zero. For example, 3/0=X and 0*X=3 are equivalent equations. Obviously, no number can be x to make this equation hold.

A similar situation will occur if zero is divided by zero. 0/0=X can be rewritten as 0*X=0. The problem here is that all numbers can satisfy this equation. X can be any number, so this equation is of little use.

But in some cases, dividing by zero is actually effective and is actually the key to solving the problem. This was Newton's idea when he invented calculus.

For example, there is an unknown curve, and you want to find the slope of the curve at a certain point. This is equivalent to finding the slope of a straight line (tangent), which only touches this point of the curve. In many cases, it is impossible to find this slope only by algebra.

But one trick is to use calculus and the "magic" of division by zero. It is easier to find the slope of a straight line (secant) with two intersections with this curve than to find this tangent directly. If the two intersections move closer and closer, they will get closer and closer to the tangent.

So, how to find the slope of secant? It's actually quite simple. Make a right triangle and divide the height by the width to get the slope.

If the two intersections are closer, the width and height of the right triangle are closer to 0 and the slope is closer to 0/0. The slope of the curve at this point can not be obtained until the two intersection points coincide. Therefore, 0/0 is meaningful in this case, which is the slope of the curve at the change point.

The result of 0/0 can be any number, but the possible answers can be narrowed by introducing some limiting factors, which is actually the limit of 0/0 infinitive in higher mathematics. Once it can be divided by zero, a whole new mathematical world will be opened.

Hope to adopt. Thank you.