It is an identity so true for all values of x. Put x=1/3. This will find you B. Then put in any other x (say x=0) to get A.
I have managed to successfully answer all of the other partial fractions questions in my textbook but can't see how the following one is done:
The denominator is factorised to:
And then the textbook has been giving the following method to allow solving for A and B as the numerators:
I am having trouble knowing what to make x to cancel out the A part and thus solve for B. To make A = 0 wouldn't x have to = 0.333...
This is the answer given in the back of the book:
Anyway, like I said, I have been OK with the other 10 or so examples but this one has thrown me off and I have spent a long time thinking about it hopefully I have just overlooked something simple.
Any help is much appreciated.