SOLUTION: Hi, i'm really stuck on this problem for partial fractions and would really appreciate the help! Find the partial fraction decomposition of the following rational expression:

Question 447148: Hi, i'm really stuck on this problem for partial fractions and would really appreciate the help!
Find the partial fraction decomposition of the following rational expression:
5x^2+x+5/x^3+x^2+2x+2
Thanks!
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Find the partial fraction decomposition of the following rational expression:

Factor the denominator, I used synthetic division
________________
-1|1 + 1 + 2 + 2
and got
= + =
If the denominators are equal the numerators equal, so we have:
5x^2 + x + 5 = A(x+1) + B(x^2+2)
:
let x=-1, then one factor will drop out, we can solve for B
5(-1)^2 - 1 + 5 = A(-1+1) + B(-1^2+2)
5 - 1 + 5 = 0 + 3B
9 = 3B
B = 3
:
Replace B with 3, Find A
5x^2 + x + 5 = A(x+1) + 3(x^2+2)
5x^2 + x + 5 = A(x+1) + 3x^2 + 6
5x^2 - 3x^2 + x + 5 - 6 = A(x+1)
2x^2 + x - 1 = A(x+1)
Factor
(2x-1)(x+1) = A(x+1)
Divide both sides by (x+1)
(2x - 1) = A
:
so we have
= +
RELATED QUESTIONS
Hi Stuck on this question Express the following as a partial fraction 3x-1/x^2+4x+4 (answered by Fombitz,solver91311)

Hi im really stuck on this question: m+10/6m=7/8 they are supposed to be fractions. Im... (answered by stanbon)

Hi, I'm struggling with this question and would really appreciate some help; In the... (answered by josgarithmetic)

Hi everyone, I'm stuck on this problem, if someone could I help I would really appreciate (answered by Alan3354)

Hi please help me and explain thorouly on how to find the equation of the line that... (answered by ankor@dixie-net.com)

Hi....I'm stuck on this problem. If you can help, I would really appreciate it. Thank... (answered by richwmiller)

Hi, I've been stuck on this problem for a while. If anyone could help me I would really... (answered by fractalier,solver91311,MathLover1)

Hi. i would like to know if anyone can help me with a problem. i dont understand what to... (answered by scott8148)

for h(x)=2x^2+6x-9 & k(x)=3x^2-8x+8 find h(x)-2k(x) I would really really... (answered by stanbon)