# Find the partial fraction

1. Mar 27, 2013

### kai92

1. The problem statement, all variables and given/known data
(x^3+4)/((x^2-1)(x^2+3x+2))

2. Relevant equations

3. The attempt at a solution
Try separating them into Ax+B and Cx+D, then expand until
(A+C)x3+(3A+B+D)x2+(2A+3B-C)x+(2B-D)
then, I was stuck. I can't find any value for A,B,C or D. Is my attempt correct or is there other way to solve it?

2. Mar 27, 2013

### SteamKing

Staff Emeritus
Look at your expansion. What must A+C equal to match the original numerator? Follow this line of reasoning for the other factors. You will wind up with a system of equations to solve.

3. Mar 27, 2013

### Staff: Mentor

Did you factor the denominator? It's not clear to me from your work that you did. The right side should look something like this:
$$\frac{A}{x - r_1} + \frac{B}{x - r_2} + \frac{C}{(x - r_2)^2} + \frac{D}{x - r_3}$$
The reason for the 3rd term above is that there is a repeated factor that is shared by the two quadratics in the denominator.