Find the Laplace transform. I'm not sure if what I have if right so far, but when I get to the bottom line I get stuck and don't know how to proceed. Please expand so I can follow along.

out TF in 1) Y US ) = ( CS ) x Ucs) yess = S + 3 X 3 5 2 + 3 5 + 27 S = 5+3 w X 3 ( s 2 + 5 + 9 ) S = 3 (s+3 ) 35 ( 5 2 + sta ) = 5+ 3 S ( 5 2 + 5+9 ) 513 = A + BS+C 5 ( 5 2 + sta ) 5 sitsta S+ 3 - A (s ? +s ta ) + ( B s t c ) s s ( S 2 + stq) S ( 5 2 + sta ) ( 5 2 + stq )s DO = A +B 2 = At c 3 3 - 9A B = - A C = 1- A A = 3 = 1 - 3 9 3 Y CS) = (3) + (- 3 ) s+ = side work 5 5 2 +s+9 roots are 2 /3 35 - 2 - 01 5 ) + 2 . 95 8 j S 3 ( 5 + 0 5 ) 2 + 2 , 9 5 8 2 1/3 5 - 2 - 3 5 + S ( s + 0 , 5 ) 2 + 2, 9582 ( s + 0 . 5 ) 2 + 2, 95 8