Page 50 - LAPLACE TRANSFORM

s + 9
F
3. (s ) =
( + ) 3 3
s

multiply each side with ( + )

s + 9 = A ( + ) + B ( + ) + C

when (s + 3) = 0

s= − 3; s + 9 = A ( + ) + B( + ) + C
−3 + 9 = C

C = 6

s + 9 = A ( + ) + B ( + ) + C

2
s + 9 = A ( + 6 + 9) + B ( + 3) + C

2
s + 9 = A + 6 + 9 + Bs + 3B + C

2
s ; 0 = A ..................................... (1)
1
s ; 1 = 6A + B ............................ (2)
0
s (without s); 9 = 9A + 3B + C ..................... (3)

C = 6 , A = 0

1 = 6A + B ............................ (2)

1 = 6(0) + B ;

B = 1

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