Question

By the method of the fractions partial determine the function f (t) of the following functions F (s).

F(s)= s^2+7s+12/(s+2)(s+4)(s+6)

F(s)= (s+3)(s+6)/s(s^2+10s+24)

F(s)= 5(s+2)^2/s(s+1)^3

F(s)= s+6/s(s+1)^2

F(s)= 27/(s+1)^3(s+4)

Answer 1

I'll do one, and you use the same method to do the others. Come on back if you get stuck, and show where things go south.

F(s)= 5(s+2)^2/s(s+1)^3
F(s) = A/s + B/(s+1) + Cx+D/(s+1)^2 + Es^2+Fs+G/(s+1)^3

place all over a common denominator s(s+1)^3 and expand the numerator, then equate coefficients of like powers of s.

You will find that most of the coefficients are zero, and you end up with
A = 20
B = -20
D = -15
G = -5

F(s) = 20/s - 20/(s+1) - 15/(s+1)^2 - 5/(s+1)^3