partial fraction reduction - help plz?

Question

How would I solve the following using partial fraction reduction to find f(t):

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

Thanks!

can i have more details plz? thanks!

Answer 1

I guess your request for more details means you do not know how to proceed even with the hint given.

s/(s + 1)^2 = a/(s + 1) + b/(s + 1)^2 = [a*(s + 1) + b]/(s + 1)^2. Because the denominators are the same in the left member and the right member, the numerators must be IDENTICALLY EQUAL. Thus,

(1) s = a*(s + 1) + b.

Let s = -1 in (1). That shows that b = -1. Now we may refine (1) to get

(2) s = a*(s + 1) - 1.

Adding 1 to both sides of (2) we see that s + 1 = a*(s + 1). We divide both sides by s + 1 and find that a = 1. The decomposition, therefore, is

s/(s + 1)^2 = 1/(s + 1) - 1/(s + 1)^2 .

Answer 2

By the rules for partial fraction reduction,

s/ (s+1)^2 = a/(s+1) + b/(s+1)^2.

Now just solve for a and b.