Partial Fraction Decomposition for Inverse Laplace Transform

[tandoorichicken]

The whole problem reads:
Find the inverse Laplace transform of
\frac{s-2}{s^3+2s^2+2s}

I think once I get the expression simplified I can do the rest by myself. I started to separate this expression out by partial fractions and got as far as this:
\frac{s-2}{s^3+2s^2+2s}=\frac{s-2}{(s^2+2s+2)s}=\frac{As+B}{s^2+2s+2} +\frac{C}{s}

(As+B)s+C(s^2+2s+2)=s-2
From this expression I got C=-1, which I checked was correct by using my calculator, but I still don't know how to find A, or B. Can anyone help with this please?

Any ideas or hints on how to do the inverse would be also be appreciated.

 

[Corneo]

Note that

s^2+2s+2 = (s+1)^2+1

Opps major brain laspe. That should be fixed

 

[whozum]

Note that

s^2+2s+2 = (s+1)^2

Nope, it equals (s+1)^2 + 1.[/tex]<br /> <br /> edit: tex

 

[Corneo]

Or perhaps that wasn't too helpful. Here is an trick I learned when doing these partial fractions problems.

Consider what you have
(As+B)s+C(s^2+2s+2)=s-2

Multiply out and gather the terms.
(A+C)s^2 + (2C+B)s + 2C = s-2

Is there a s^2 term on the right hand side of the equation? What does this tell you about A+C? What about 2C, what should that be equal to? And 2C+B?

 

[tandoorichicken]

Thanks, Corneo.