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Find the inverse laplace transform of (s2−4s−5)/(s2−4s−5)(s^2- 4s - 5)/(s^2 -4s-5)

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Full solution

Q. Find the inverse laplace transform of (s2−4s−5)/(s2−4s−5)(s^2- 4s - 5)/(s^2 -4s-5)
  1. Simplify the function: The given function is (s2−4s−5)/(s2−4s−5)(s^2 - 4s - 5)/(s^2 - 4s - 5). To find the inverse Laplace transform, we simplify the function.\newlineCalculation: (s2−4s−5)/(s2−4s−5)(s^2 - 4s - 5)/(s^2 - 4s - 5) simplifies to 11, since the numerator and denominator are identical.
  2. Find inverse Laplace transform: Now that we have the simplified function, which is 11, we can find the inverse Laplace transform of 11. The inverse Laplace transform of 11 is the delta function, δ(t)\delta(t), which represents an impulse at time t=0t = 0.

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