by the way thanks very much for telling me that 'A' and 'B' represents polynomials.never knew it before.
It's not surprising - you're trying to teach yourself, and it's always going to be that there are gaps. You need properly constructed tutorials and exercises.
Have a look at these:
http://www.google.co.uk/#q=algebra+tutorial+with+exercises
Pick one of the tutorials and work through it completely. Then you can do a google search for partial fraction tutorials and do the same.
by the way i'am not offended.i'am enjoying myself with calculus.i'll get back to you if i have any doubts.if you got to say something you can.
As a final hint, here's something interesting:
For a polynomial p(x), if p(a)=0 for some value a,
then (x-a) is a factor of p(x).
That means, for example, that (x+1) is a factor of
x^3+1 and (x-1) is a factor of x^3-1.