(adsbygoogle = window.adsbygoogle || []).push({}); Separating a fraction

I don't remember what this method is named in English, but I want to write the fraction

[tex]\frac{1}{(s^2 + 1)(s-3)(s+2)}[/tex]

in the form

[tex]\frac{A}{s^2 + 1} + \frac{B}{s-3} + \frac{C}{s+2}[/tex]

I multiply A with (s-3)(s+2), B with (s^2 + 1)(s+2) and C with (s^2 + 1)(s-3), to get

[tex]As^2 - As - 6A + Bs^3 + 2Bs^2 + Bs + 2B + Cs^3 - 3Cs^2 + Cs - 3C = 1[/tex]

and the equations

(1) B + C = 0

(2) A + 2B - 3C = 0

(3) -A + B + C = 0

(4) -6A + 2B - 3C = 1

(1) and (3) gives A = 0

(2) then gives B = C = 0

This is obviously wrong. The correct answer is

A = 2s - 4

B = 2

C = -4

according to my book. There must be something I don't understand here...

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# Homework Help: Laplace transformations

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