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Suppose I have a fraction as

$$\frac{1}{s}\frac{1}{s^2-2s+5}$$

So that:

$$1 = (A+B)s^2+(C-2A)s+5A$$

I'm just confused as to how I can solve for $A,B,$ and $C$. I know if we plug $s=0$ we get $A = \frac{1}{5}$, but what can I do for B and C?

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2 Answers

up vote 2 down vote accepted

Both sides of the equation are polynomials in $s$ (the LHS just happens to be a constant polynomial), so you can compare coefficients of $s^2$ on both sides. The coefficient of $s^2$ is zero on LHS and $A+B$ on RHS. So $A+B=0$. Do the similar for the coefficient of $s$.

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+1 for explaining why $A + B = 0$. –  Code-Guru Dec 14 '12 at 2:23
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You have $A + B = 0$ and $C - 2A = 0$. Use 'em.

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You mean $C - 2A=0$ –  Robert Israel Dec 14 '12 at 1:52
    
Thanks, Robert. –  ncmathsadist Dec 14 '12 at 1:54
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