s^{2}F(s) + sF(s) - 6F(s) = (s^{2}+4)/(s^{2}+s) Solve for L^{-1}{F}

Attempt:

Simplified the equation to F(s) = (s^{2}+4)/[s*(s+1)*(s+3)*(s-2)]

Fraction Decomposition s^{2}+4 = A(s+1)(s+3)(s-2) + B*s(s+3)(s-2) + C*s(s+1)(s-2) + D*s(s+1)(s+3)

For s = 0 ----> -6A = 4 ----> A = -2/3

For s = -1 ----> 6B = 5 ----> b = 5/6

For s = -3 ----> -30C = 13 ----> C = -13/30

For s = 2 ----> 30D = 8 ----> D = 4/15

Inverses I get:

A: -2/3

B: 5/6 * e^{-t }C: -13/30 * e^{-3t}

D: 4/15 * e^{2t}

----> L^{-1}{F} = -2/3 + 5/6 * e-t + -13/30 * e^{-3t }+ 4/15 * e^{2t}where s > -3

I think I have an error in my factoring, but I am not sure. Could anyone help me out with this?