I'm not a big math person (working on it) but I have a question that has puzzled me for a while now. How is it possible for an equation at a certain number x to be unsolvable (0 denominator) yet after you factor the equation out a bit, all of a sudden it has an answer. This seems to violate some basic rule of an equation should always equal the same thing. For instance

x^2-x-6

________

x-3

at x=3 you get 0 / 0 which obviously does not exist.

However, if you factor it to

(x-3)(x+2)

________

x-3

and remove the x-3's then you have a perfectly solvable x+2 or (5).

How is this possible? How can I change the answer of the equation just by simplifying it?

sorry for the noob question, but I really would like to understand this.