Question

Find the inverse transform
F(s) = (s+4) / s²+6s+13

Answer 1

To find the inverse transform of F(s) = (s+4) / (s²+6s+13), you can use partial fraction decomposition.

Step-by-step explanation:

To find the inverse transform of F(s) = (s+4) / (s²+6s+13), you can use partial fraction decomposition. First, factor the denominator: s²+6s+13 = (s+3)(s+2)+7. Then, you can write the expression as:

F(s) = (s+4) / ((s+3)(s+2)+7) = A / (s+3) + B / (s+2) + C / ((s+3)(s+2)+7)

Now, multiply both sides of the equation by the denominator (s+3)(s+2)+7 and solve for A, B, and C. Once you have the values of A, B, and C, you can rewrite the expression as:

F(s) = A / (s+3) + B / (s+2) + C / ((s+3)(s+2)+7)