determine 1)L^− [((4s^2 −17s−24)/(s(s+3)(s−4)))] 2)L^− [((5s^2 −4s−7)/((s−3)(s^2 +4)))]


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Question Number 180145 by ali009 last updated on 07/Nov/22

$d e t e r m i n e$ $1) L^{-} [\frac{4 s^{2} - 17 s - 24}{s (s + 3) (s - 4)}]$ $2) L^{-} [\frac{5 s^{2} - 4 s - 7}{(s - 3) (s^{2} + 4)}]$
	Answered by Ar Brandon last updated on 08/Nov/22

	$L^{- 1} (\frac{4 s^{2} - 17 s - 24}{s (s + 3) (s - 4)})$ $= L^{- 1} (\frac{2}{s} + \frac{3}{s + 3} - \frac{1}{s - 4})$ $= 2 + 3 e^{- 3 t} - e^{4 t}$ $L^{- 1} (\frac{5 s^{2} - 4 s - 7}{(s - 3) (s^{2} + 4)})$ $= L^{- 1} (\frac{2}{s - 3} + \frac{3 s + 5}{s^{2} + 4})$ $= L^{- 1} (\frac{2}{s - 3} + \frac{3 s}{s^{2} + 4} + \frac{5}{s^{2} + 4})$ $= 2 e^{3 t} + 3 \cos (2 t) + \frac{5}{2} \sin (2 t)$
	Commented by ali009 last updated on 08/Nov/22

	$t h a n k y o u$
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