L ^-1{5s^2+3s-16/(s-1)(s-2)(s+3)}

asked by guest
on Nov 24, 2024 at 1:00 am



You asked:

Evaluate the expression: \({L}^{-1} \cdot \left(5 {s}^{2} + 3 s - \frac{16}{\left(s - 1\right) \cdot \left(s - 2\right) \cdot \left(s + 3\right)}\right)\)

MathBot Answer:

Evaluated



\(\displaystyle {L}^{-1} \cdot \left(5 {s}^{2} + 3 s - \frac{16}{\left(s - 1\right) \cdot \left(s - 2\right) \cdot \left(s + 3\right)}\right) = \frac{5 s^{2} + 3 s - \frac{16}{\left(s - 2\right) \left(s - 1\right) \left(s + 3\right)}}{L} \)

Expanded

\[{L}^{-1} \cdot \left(5 {s}^{2} + 3 s - \frac{16}{\left(s - 1\right) \cdot \left(s - 2\right) \cdot \left(s + 3\right)}\right) = - \frac{16}{s^{3} L - 7 L s + 6 L} + \frac{5 s^{2}}{L} + \frac{3 s}{L}\]

Factored

\[{L}^{-1} \cdot \left(5 {s}^{2} + 3 s - \frac{16}{\left(s - 1\right) \cdot \left(s - 2\right) \cdot \left(s + 3\right)}\right) = \frac{5 s^{5} + 3 s^{4} - 35 s^{3} + 9 s^{2} + 18 s - 16}{L \left(s - 2\right) \left(s - 1\right) \left(s + 3\right)}\]

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