SOLUTION: 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)

Question 467157: 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 by robertb(5830) (Show Source): You can put this solution on YOUR website!
should have been written as , and then equated to . Compare term-by-term to get the system
A + B = 5,
2A + B + C = 20,
A = 6.
==> B = -1, and C = 9.
RELATED QUESTIONS
Partial fraction decomposition 2x^2 -x +4 / x^3 +4x I put irreducible and got it... (answered by josgarithmetic,MathTherapy)

Evaluate by partial fraction... (answered by Fombitz)

find the partial fraction decomposition :... (answered by Edwin McCravy)

Write the partial fraction decomposition of each rational expression. x/x^2-5x+6 (answered by robertb)

I have to use the FOIL to find the product. Express the product as descending powers of... (answered by Theo)

Solve for x 3(x-6)=2(x+2) I have tried this a couple different times and this is as... (answered by Earlsdon)

I am having the hardest time with this one. When I try to plug in x it does not work for (answered by rapaljer)

Given the function (x^(4)-2x^(3)+x^(2)+5x-1)/x^(2)-2x+1 Write the form of the... (answered by josgarithmetic)

2(x-3)=5x+4 solve for x Here is what I have so far 2x-6=5x+4 +6 +6 2x=5x+10... (answered by ReadingBoosters,littlebitlove)