Question

For the function F (s) = (s^2+s+1)/s(s+5)(s+3), after splitting this function into partial fractions, the co-efficient of 1/(s+5) is?

(a) 1.1

(b) 2.1

(c) 3.1

(d) 4.1

The question was posed to me in unit test.

My doubt is from Inverse Transforms in section Intoduction to the Laplace Transform of Network Theory

Answer 1

The correct option is (b) 2.1

For explanation: To obtain the constant B, multiply the given equation with (s+5) and putting s = -5. B = (s + 5)F (s) |s=-5 = (s^2+s+1)/s(s+3)|s=-5 = 2.1.