find L ^ - 1 * [(6 ^ 2 +

2s - 4)/((s - 5)(s ^ 2 + 9))]

asked by guest
on Nov 17, 2024 at 2:56 am



You asked:

Evaluate the expression: \({L}^{-1} \cdot \frac{{6}^{2} + 2 s - 4}{\left(s - 5\right) \cdot \left({s}^{2} + 9\right)}\)

MathBot Answer:

Evaluated



\(\displaystyle {L}^{-1} \cdot \frac{{6}^{2} + 2 s - 4}{\left(s - 5\right) \cdot \left({s}^{2} + 9\right)} = \frac{2 s + 32}{L \left(s^{2} + 9\right) \left(s - 5\right)} \)

Expanded

\[{L}^{-1} \cdot \frac{{6}^{2} + 2 s - 4}{\left(s - 5\right) \cdot \left({s}^{2} + 9\right)} = \frac{2 s}{s^{3} L - 5 s^{2} L + 9 L s - 45 L} + \frac{32}{s^{3} L - 5 s^{2} L + 9 L s - 45 L}\]

Factored

\[{L}^{-1} \cdot \frac{{6}^{2} + 2 s - 4}{\left(s - 5\right) \cdot \left({s}^{2} + 9\right)} = \frac{2 \left(s + 16\right)}{L \left(s^{2} + 9\right) \left(s - 5\right)}\]

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