Question

Partial fraction decomposition....
Again, I went wrong somewhere. Not sure why I am not getting this...

Partial fraction decomposition:
(5x^2+20x+6)/x^3+2x^2+x

Here's what I got but I think it is wrong:
(5x^2+20x+6)/x(x^2+2x+1)
(5x^2+20x+6)/x(x+1)^2
(A/x)+(B/(x+1))+(C/(x+1)^2)
A(x+1)(x+1)^2 + B(x)(x+1)^2 + C(x)(x+1)

(5x^2+20x+6)=Ax^3+Bx^3+3Ax^2+2Bx^2+Cx^2+3Ax+Bx+Cx+A

(5x^2+20x+6)=x^3(A+B) + x^2(3A+2B+C) + x(3A+B+C) + A


A+B=0
3A+2B+C=5
3A+B+C=20
A=6

A=6
B=-6
C=-1

But this isn't right. Where did I go wrong?

Answer 1

why do you expand them for starters?

Answer 2

(5x^2+20x+6)/x(x+1)^2=(A/x)+(B/(x+1))+(C/(x+1)^2)

(5x^2 +20x +6 = A(x+1)^2 +Bx(x+1) + C(x)

Answer 3

u made alot of mistakes :|

Answer 4

^% thats correct

Answer 5

sub x=0:

6 = A

A+6 .

Answer 6

sub x=-1 :

5 -20+6 = -C

C= 9

Answer 7

sub x=1 :

31= 4A+2B+C

B = (31-4A-C) / 2 = (31-24 -9) / 2 = -1

Answer 8

A=6, B=-1, C=9

Answer 9

comparing coeffiecents is a very long method and bound to make tons of mistakes