
Partial fraction
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 (xa). We work in real numbers, and P is decomposable in R.
Q(x)/P(x) = A/(xa) + B/(xb) ... etc
So people tell me that now we multiply by P(x), make Q(x) = A* [P(x)/(xa)] + B * [P(x)/(xb)] ... ,
then suppose x = a (that is in order to eliminate the term including A) and so on.
How come we multiply by (xa) but don't say that a is a prohibited value for x? (Thinking)

Please do not post algebra problems in the wrong subforum, head over to the pre university forum, and post this problem in the algebra section.
You will also get quicker results.
*tip: use latex, your question is very confusing.