Need help with partial fraction decomposition for inverse Laplace?

[rforrevenge]

Homework Statement

I want to decompose this (s+2)*(s+1)/(s+2)*(s+1)*(s^2+1)-1 using partial fractions so after that i can inverse Laplace it. I have been working on it for several hours but i cannot find a solution. Any help?

Homework Equations

The Attempt at a Solution

 

[Unco]

Use parentheses so that it is clear what the expression, in particular what the denominator, is. Is it: (s+2)*(s+1)/[(s+2)*(s+1)*(s^2+1)] - 1? Presumably not, as trivially (s+2)*(s+1)/[(s+2)*(s+1)*(s^2+1)] - 1 = 1/(s^2+1) - 1.

 

[rforrevenge]

The fraction is: (s+2)*(s+1)/[(s+2)*(s+1)*(s^2+1)-1]

The -1 is a part of the denominator

 

[Unco]

Thanks for clarifying, rforrevenge. The denominator (s+2)*(s+1)*(s^2+1)-1 doesn't appear to factorise, so no partial fraction decomposition is possible. Check your work up to arriving at, presumably, Y(s) = (s+2)*(s+1)/[(s+2)*(s+1)*(s^2+1)-1]. Perhaps show us how you arrived at it.

 

[gabbagabbahey]

Are you sure you've copied down the correct expression? The denominator expands to s^4+3s^3+3s^2+3s+1 which has no real roots/factors.

 

[rforrevenge]

Yes i am sure.I found out that the denominator has no roots,so there must be some problem with that expression our prof. gave us