Question

Find the \(L^{-1} \left (\frac{(s+1)}{(s+2)(s+3)}\right )\).

(a) 2e^-3t-e^-2t

(b) 3e^-3t-e^-2t

(c) 2e^-3t-3e^-2t

(d) 2e^-2t-e^-t

This question was addressed to me in an online interview.

The query is from General Properties of Inverse Laplace Transform in chapter Laplace Transform of Engineering Mathematics

Answer 1

Correct option is (a) 2e^-3t-e^-2t

The best I can explain: In the given question,

\(L^{-1} \left (\frac{(s+1)}{(s+2)(s+3)}\right )=L^{-1} \left (\frac{2(s+2)-(s+3)}{(s+2)(s+3)}\right )\)

=\(L^{-1} \left (\frac{2}{(s+3)}\right )+L^{-1} \left (\frac{1}{(s+2)}\right )\)

=2e^-3t-e^-2t.