# Thread: I do not understand partial fraction decomposition.

1. ## I do not understand partial fraction decomposition.

At all. I have a test on it tomorrow, and this is mightily distressing, to say the least.

If someone could give me clear instructions on how to solve these kinds of problems?
Or give clear steps on how to solve this:
(4x^2+2x-1)/[x^2(x+1)]

Thank you ahead of time for any help!

2. Originally Posted by flyingsquid
At all. I have a test on it tomorrow, and this is mightily distressing, to say the least.

If someone could give me clear instructions on how to solve these kinds of problems?
Or give clear steps on how to solve this:
(4x^2+2x-1)/[x^2(x+1)]

Thank you ahead of time for any help!
$\displaystyle \equiv \frac{A}{x} + \frac{B}{x^2} + \frac{C}{x+1}$.

Now get the values of A, B and C:

$\displaystyle 4x^2 + 2x - 1 \equiv Ax(x+1) + B(x+1) + Cx^2$.

Substitute x = -1: 1 = C.

Substitute x = 0: -1 = B.

Substitute x = 1: 5 = 2A + 2B + C => A = 3 (using the known values of B and C).