Question

Find inverse laplace transform

(2s-56)/(s^2-4s-12)

Answer 1

$\frac{2s-56}{s^2-4s-12}=\frac{2s-56}{(s+2)(s-6)}=\frac{15}{2(s+2)}-\frac{11}{2(s-6)}$

$L^{-1}(\frac{15}{2(s+2)}-\frac{11}{2(s-6)})=\frac{15}{2}e^{-2t}-\frac{11}{2}e^{6t}.$