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Solve this equation with partial fractions?

Posted 2 months ago
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I have this quotient 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 success.

Thank you very much.

Could use SolveAlways to eliminate s and solve for the rest.

SolveAlways[(s^2 + 3)/((s - 1)^2 (s + 1)) == 
  A1/(s - 1) + A2/(s - 1)^2 + A3/(s + 1), s]

(* Out[9]= {{A2 -> 2, A3 -> 1, A1 -> 0}} *)

Alternatively could get the PFD directly with Apart.

Apart[(s^2 + 3)/((s - 1)^2 (s + 1)), s]

(* Out[8]= 2/(-1 + s)^2 + 1/(1 + s) *)
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