Find the inverse Laplace transform of F(s) = e^(-6s) / (s^2 + 3s - 4) f(t) = ? (Use step(t-c) for u_c(t).)
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Step 1:** Apply partial fraction decomposition to the expression \( \frac{1}{s(s-1)(s+4)} \): \[ \frac{1}{s(s-1)(s+4)} = \frac{A}{s} + \frac{B}{s-1} + \frac{C}{s+4} \] \[ 1 = A(s-1)(s+4) + B(s)(s+4) + C(s)(s-1) \] ** Show more…
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