Hi everyone. I have a question that is troubling me.

Let's have a rational function, for example Q(x)/P(x), and decide for some reason to decompose it into a lovely sum of constants over expressions of the type (x-a). We work in real numbers, and P is decomposable in R.

Q(x)/P(x) = A/(x-a) + B/(x-b) ... etc

So people tell me that now we multiply by P(x), make Q(x) = A* [P(x)/(x-a)] + B * [P(x)/(x-b)] ... ,

then suppose x = a (that is in order to eliminate the term including A) and so on.

How come we multiply by (x-a) but don't say that a is a prohibited value for x?