求拉氏反变换(s+2)/(s*s+4s+3)的解法

Question

求拉氏反变换 (s+2)/(s*s+4s+3)的解法

Answer 1

(s+2)/(s²+4s+3)
=(s+2)/[(s+1)(s+3)]
=A/(s+1) + B/(s+3)
合并后比较系数得：A=1/2,B=1/2
因此原式=(1/2)[1/(s+1) + 1/(s+3)]

因此逆变换为：(1/2)[e^(-t) + e^(-3t)]