Question

Having trouble with the partial fraction decomposition of (4s-8)/[(s)(s+1)(s^2+1)]. Here's what I have so far:

A/s+B/(s+1)+Cs/(s^2+1)+D/(s^2+1)=(4s-8)/[(s)(s+1)(s^2+1)]

A(s+1)(s^2+1)+B(s)(s^2+1)+Cs(s)(s^2+1)+D(s)(s+1)=4s-8

Let s=0: A=-4
Let s=-1: B=6

-4s^3-4s^2-4s-4+6s^3+6s=s^3(C)+s^2(C+D)+s(D)=4s-8

s^3(C)+s^2(C+D)+s(D)=-2s^3+4s^2+2s-4

from s^3(C)=-2s^3: C=-2
from s(D)=2s: D=2

but s^2(C+D)=4s^2, and C+D=0 from the above values

Please help.

Answer 1

laplace transformations?

Answer 2

yep

Answer 3

hold on, this is two bad for latex, ill grab a pen

Answer 4

alright thank you

Answer 5

its going to take me a min, the wife is making me make her a grilled cheese, but check back in a bit

why did you do two fractions with s^2+1 in the denom?

Answer 6

I just split up (Cs+D)/(s^2+1).

Answer 7

ahh

Answer 8

brb

Answer 9

Aight.

Answer 10

By the way , welcome to Openstudy

Answer 11

Thanks man. Glad I found this site.

Answer 12

yes , this is an awesome site

Answer 13

I'm guessing this is a simple algebra mistake, but damn, I can't find it.

Answer 14

Shouldn't A be -8?

Answer 15

yes

Answer 16

Oh...For some reason I added 1+1 instead of multiplying.

Answer 17

Thanks for the help! I really appreciate it! Sometimes it's hard to catch your own mistakes.

Answer 18

You are welcome.

Answer 19

^ I agree lol