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Hello all,

Having difficulty with this one question that involves complex roots. Here it is:

[tex]F(s)=\frac{s+3}{s^3+3s^2+6s+4}[/tex]

I tried two different ways to tackle it. First method I divided it right away:

[tex]F(s)=\frac{s+3}{s^3+3s^2+6s+4}\rightarrow{s^2+6-\frac{14}{s+3}}[/tex]

Is there some sort of approach to something like s^2? I have not taken a differential equations course, and this is in one of my classes for modelling circuits.

If I decide not to do it this way, I can break it up via partial fractions:

[tex]F(s)=\frac{s+3}{s^3+3s^2+6s+4}=\frac{s+3}{(s+1)(s+1-\sqrt{3}j)(s+1+\sqrt{3}j)}=\frac{A}{s+1}+\frac{B}{s+1-\sqrt{3}j}+\frac{C}{s+1+\sqrt{3}j}[/tex]

where j is a complex number.

Thus,

[tex]A(s^2+2s+4)+B(s+1)(s+1+\sqrt{3}j)+C(s+1)(s+1-\sqrt{3}j)=s+3[/tex]

[tex]As^2+Bs^2+Cs^2=A+B+C=0[/tex]

The part that I do not know how to do is from here.

Would it be:

[tex]2As+2Bs+2Cs+j\sqrt{3}Bs+j\sqrt{3}Cs=s[/tex]

or are the complex numbers treated separetely?

Or is there an easier way, altogether?

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# Inverse Laplace Transform

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