Can anyone explain a simple method for performing partial fraction decomposition relative to Laplace Transformations?

Question

anonymous · Answer

why yes i can good sir!! but it works best with an example

anonymous · Answer

gimme a sec. i shall return.

anonymous · Answer

no particular example actually, i'm just trying to figure out a quick method for 
breaking down annoying laplace transforms :P

anonymous · Answer

lol, i hear ya, i hate those things. annoy my balls off.

anonymous · Answer

$$(s+3) \div s ^{2}(s+1)(s+2)$$

anonymous · Answer

that would be a nice one to see performed

anonymous · Answer

done and done, sec. responding to another Q

anonymous · Answer

kk, no rush

anonymous · Answer

ok, so we have s+3/(s^2(s+1)(s+2)) yes? so we can set up our equation as follows:

s+3/(s^2(s+1)(s+2))= A/(s)+ Bx+C/s^2 + D/(s+1) + E/(s+2)

anonymous · Answer

sec

zarkon · Answer

Just use WolframAlpha http://alturl.com/idnwj ;)

anonymous · Answer

ok, so remember that any time you have an s^2 in the denominator, you need to have As+B in the numerator, instead of just a single variable. and if it's a s^3 in the denominator it's an As^2+Bs+C in the numerator, etc, etc.

anonymous · Answer

i noticed you used A/s + (Bs+C)/s^2

is that necessary?  seems redundant

anonymous · Answer

yeah, it is necessary, otherwise you miss a term in your differential equation. also any time you have something like (s+2)^2 you have to have A/(s+2) + Bs+C/(s+2)^2

zarkon · Answer

oh..no!!

zarkon · Answer

A/s+B/s^2 is fine

anonymous · Answer

but (Bs+C)/s^2 = B/s + C/s^2

then A/s + B/s combine.  when you transform back from laplace, you factor out the constant anyways.

These are the things that confuse me lol

anonymous · Answer

is it?! ahh!!! i suck tonight.lol. i apologize for misleading

anonymous · Answer

zarkon wins all the internets for catching that.

anonymous · Answer

I may just have to look for an app for my ti-89.  such a thing should exist

zarkon · Answer

when you have something like $$(s+2)^3$$

you get 

$$\frac{A}{s+1}+\frac{B}{(s+2)^2}+\frac{C}{(s+2)^3}$$

zarkon · Answer

use the expand command

anonymous · Answer

I never could get expand to work the way I needed it too.  Time to fish out that booklet

now where the hell is it at lol.  anyways, thanks for the help