How do you express as a partial fraction $\frac{1}{{(s^{2} + 1)}^{2}}$ $1/(s^2 +1)^2$ ?

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How do you express as a partial fraction $\frac{1}{{(s^{2} + 1)}^{2}}$ $1/(s^2 +1)^2$ ?

1 Answer

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Answer 1 · 2015-09-26T04:42:19

The expression cannot be further decomposed.

Explanation:

We can try to find a partial fraction decomposition by finding $A, B, C, and D$ $A, B, C, " and "D$ so that:

$\frac{A s + B}{s^{2} + 1} + \frac{C s + D}{{(s^{2} + 1)}^{2}}$ $(As+B)/(s^2+1) +(Cs+D)/(s^2+1)^2$ (as the method tells us to do),
But we get $A = 0$ $A=0$ , $B = 0$ $B=0$ , $C = 0$ $C=0$ and $D = 1$ $D=1$ , which is what we started with.

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How do you express as a partial fraction $\frac{1}{{(s^{2} + 1)}^{2}}$ $1/(s^2 +1)^2$ ?

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How do you express as a partial fraction $\frac{1}{{(s^{2} + 1)}^{2}}$ $1/(s^2 +1)^2$ ?