# Thread: The form of a partial fraction decomposition

1. ## The form of a partial fraction decomposition

For the following problem provide the "form" of the partial fraction decomposition for the given fractional expression. You do not have to solve the undetermined coefficients.
4. 2x^2 - 3x + 8 / x^3 + 9x
I took an x out and it's no x(x^2+9) My answer is A/X + BX+C/x^2+9

5. x- 7 / x^4 - 16
I did (x^2+4)(x^2-4). I factor (x^2 - 4) into (x-2)(x+2). My answer is AX+B/x^2+4 + C/(x+2) + D/(x-2)

6. x^2 - 4x + 6 / (x+3)^2 (x^2+1)^2.
My answer is A/(x+3) + B/(x+3) + CX+D/(x^2+1) + EX+F/(x^2+10^2)
Here's a scan of the problems.
http://pic20.picturetrail.com/VOL137.../392720956.jpg

2. Hello, rowdy3!

For the following problems, provide the form of the partial fraction decomposition.

$\displaystyle 4.\;\;\dfrac{2x^2 - 3x + 8}{x^3 + 9x}$

My answer: .$\displaystyle \dfrac{A}{x} + \dfrac{Bx+C}{x^2+9}$

$\displaystyle 5.\;\;\dfrac{x- 7}{x^4 - 16}$

My answer: .$\displaystyle \dfrac{Ax+B}{x^2+4} + \dfrac{C}{x+2} + \dfrac{D}{x-2}$

$\displaystyle 6.\;\;\dfrac{x^2 - 4x + 6}{(x+3)^2(x^2+1)^2. }$

My answer: .$\displaystyle \dfrac{A}{x+3} + \dfrac{B}{(x+3)^2} + \dfrac{Cx+D}{x^2+1} + \dfrac{Ex+F}{(x^2+1)^2}$

Correrct! . . . Good work1