What is inverse oflaplace (s+3)/(s+5) ?

The answer to inverse oflaplace (s+3)/(s+5) is \delta(t)-2e^{-5t}

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inverse oflaplace (s+3)/(s+5)

inverse laplace

\frac{s + 3}{s + 5}

δ (t) - 2 e^{- 5 t}

Solution steps

L^{- 1} {\frac{s + 3}{s + 5}}

Take the partial fraction of

\frac{s + 3}{s + 5} : 1 - \frac{2}{s + 5}

= L^{- 1} {1 - \frac{2}{s + 5}}

Use the linearity property of Inverse Laplace Transform:

For functions

f (s), g (s)

and constants

a, b : L^{- 1} {a \cdot f (s) + b \cdot g (s)} = a \cdot L^{- 1} {f (s)} + b \cdot L^{- 1} {g (s)}

= L^{- 1} {1} - L^{- 1} {\frac{2}{s + 5}}

L^{- 1} {1} : δ (t)

L^{- 1} {\frac{2}{s + 5}} : 2 e^{- 5 t}

= δ (t) - 2 e^{- 5 t}

\int e^{i 7 x} cos (3 x) d x

\int_{- 2}^{1} (2 x^{2} + 3) d x

\frac{d}{d x} (1 + cos (x))

\int 4 x + 3 d x

\frac{d}{d x} (- sin (2 x) - 2 cos (x))

What is inverse oflaplace (s+3)/(s+5) ?
The answer to inverse oflaplace (s+3)/(s+5) is \delta(t)-2e^{-5t}