How to Correctly Approach Partial Fraction Decomposition?

[kai92]

Homework Statement

(x^3+4)/((x^2-1)(x^2+3x+2))

Homework Equations

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?

 

[SteamKing]

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.

 

[Mark44]

Homework Statement

(x^3+4)/((x^2-1)(x^2+3x+2))

Homework Equations

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?

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.