# 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) *)