Partial Fraction Decomposition

[ns5032]

Homework Statement

I am just trying to do partial fraction decomposition on an equation. I'm not too good with it, as far as knowing if I need just A or Ax+B, etc.

[e^(-2s) / (s^2+1)(s-1)(s+1)^2]

Homework Equations

The Attempt at a Solution

I'm not quite sure how to work with the e^-2s, but as far as doing the partial fractions, is this right: ?

Ax+B/(s^2+1) + C/(s-1) + D/(s+1) + E/(s+1)

I really just need help with that first step, making sure I set it up right, and also on how to deal with the e^(-2s). Do I take it out and treat it as 1? Do I set what I get from the partial fraction decomposition equal to e^(-2s) or something else??

Thanks!

 

[HallsofIvy]

Homework Statement

I am just trying to do partial fraction decomposition on an equation. I'm not too good with it, as far as knowing if I need just A or Ax+B, etc.

[e^(-2s) / (s^2+1)(s-1)(s+1)^2]

Homework Equations

The Attempt at a Solution

I'm not quite sure how to work with the e^-2s, but as far as doing the partial fractions, is this right: ?

Ax+B/(s^2+1) + C/(s-1) + D/(s+1) + E/(s+1)

The last one should be E/(s+1)^2.

I really just need help with that first step, making sure I set it up right, and also on how to deal with the e^(-2s). Do I take it out and treat it as 1? Do I set what I get from the partial fraction decomposition equal to e^(-2s) or something else??

Thanks!

No, you do not treat e^(-2s) as 1- it isn't!
You write
[tex]\frac{e^{-2s}}{(s^2+1)(s-1)(s+1)^2}= \frac{As+B}{s^2+1}+ \frac{C}{s-1}+ \frac{D}{s+1}+ E/(s+1)^2[/itex]
for all x and solve for A, B, C, D, E.

Probably the simplest way is to multiply both sides by $(s^2+ 1)(s- 1)(s+1)^2$ to get rid of the fractions, then take s equal to whatever 5 numbers you wish so you get 5 equations to solve.