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 the term 1/s is?

(a) 1/5

(b) 1/10

(c) 1/15

(d) 1/20

This question was posed to me in an interview for internship.

This intriguing question comes from Inverse Transforms topic in division Intoduction to the Laplace Transform of Network Theory

Answer 1

Correct answer is (c) 1/15

For explanation: To obtain the constant A, multiply the given equation with (s) and putting s = 0. The co-efficient of the term 1/s is A = sF (s)|s=0 = (s^2+s+1)/(s+5)(s+3)|s=0 =1/15.