Question

partial decomposition:

Answer 1

\[Y=\frac{10s^3 +54s^2 +185s+216}{(s^2 +4)(s^2 +4s+13)}\]

Answer 2

\[\frac{As+B}{s^{2}+4} +\frac{Cs+D}{s^{2}+4s+13}\]
A+C = 10
4A+B+D = 54
13A+4B+4C = 185
13B+4D = 216

solve system of equations

Answer 3

http://www.wolframalpha.com/input/?i=a%2Bc%3D10%2C+4a%2Bb%2Bd%3D54%2C13a%2B4b%2B4c%3D185%2C13b%2B4d%3D216

sorry im tired and don't want to do it by hand