Question

Find the inverse Laplace of
G(s)=(s²+3s+10)(s+5)/(s+3)(s+4)(s²+2s+100)

Answer 1

To find the inverse Laplace transform, factorize the denominator and express the function as the sum of fractions. Apply the inverse Laplace transform to each term and combine the results.

Step-by-step explanation:

The inverse Laplace transform of a rational function is found by completing partial fraction decomposition. First, factorize the denominator (s+3)(s+4)(s²+2s+100) completely. Then, express the original function (s²+3s+10)(s+5) as the sum of fractions with these factors as denominators. Next, apply the inverse Laplace transform to each term separately. Finally, combine the results to find the inverse Laplace transform of the original function.