Message Boards Message Boards

0
|
6534 Views
|
3 Replies
|
0 Total Likes
View groups...
Share
Share this post:

Find the constants in partial fractions?

Chiel Geeraert
Posted 6 years ago

I have this quotiënt split in partial fractions as following :

(s^2 + 3) / ((s - 1)^2 (s + 1)) ==  A1 / (s - 1) + A2 / (s - 1)^2  + A3 / (s + 1)

Is there an easy way to find the constants ? I tried several things with Solve but without succes.

Thank you very much
POSTED BY: Chiel Geeraert
3 Replies
Sort By:

Have you looked at Apart?

Apart[(s^2 + 3)/((s - 1)^2 (s + 1))] (* 2/(-1+s)^2+(1+s)^(-1) *)
POSTED BY: Tim Laska
Michael Helmle
Michael Helmle
Posted 6 years ago 
eq1 = (s^2 + 3)/((s - 1)^2 (s + 1)) ==  A1/(s - 1) + A2/(s - 1)^2 + A3/(s + 1)

sol = SolveAlways[eq1, s][[1]]

(* {A2\[Rule]2,A3\[Rule]1,A1\[Rule]0}*)

Simplify[eq1 /. sol]
POSTED BY: Michael Helmle
Chiel Geeraert
Chiel Geeraert
Posted 6 years ago

Thank you both very much. I have found a solution myself but with more 'hassle' around it then yours.

f[s_] := (s^2 + 3) / ((s - 1)^2 (s + 1)) == A1 / (s - 1) + A2 / (s - 1)^2 + A3 /( s + 1)

Solve[ { f[s] /. s -> 0, f[s] /. s -> 2, f[s] /. s -> 3}, {A1, A2, A3}]

{{A1 -> 0, A2 -> 2, A3 -> 1}}

Greetings,Chiel Geeraert (Netherlands)

POSTED BY: Chiel Geeraert
Reply to this discussion
Community posts can be styled and formatted using the Markdown syntax.
Tag limit exceeded
Note: Only the first five people you tag will receive an email notification; the other tagged names will appear as links to their profiles.
Reply Preview
Attachments
Remove
or Discard

Group Abstract Group Abstract