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# What is the partial fraction expansion of 100 / ((s^2)(s+5)) ?

100 / ((s^2)(s+5)) ?

not sure how to approach the s^2

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- kbLv 71 decade agoFavorite Answer
The s^2 denotes a repeated factor of the linear factor s.

==> 100/[s^2 (s + 5)] = A/s + B/s^2 + C/(s + 5) for some A,B,C.

To find A,B,C, clear the denominators.

100 = As(s + 5) + B(s + 5) + Cs^2.

If s = 0, then 100 = 5B.

==> B = 20.

If s = -5, then 100 = 25C.

==> C = 4.

If s = 1, then 100 = 6A + 6B + C = 6A + 6(20) + 4.

==> A = -4.

Therefore,

100/[s^2 (s + 5)] = -4/s + 20/s^2 + 4/(s + 5).

I hope that helps!

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