What is inverse oflaplace (s+2)/(s+4) ?

The answer to inverse oflaplace (s+2)/(s+4) is \delta(t)-2e^{-4t}

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inverse oflaplace (s+2)/(s+4)

inverse laplace

\frac{s + 2}{s + 4}

δ (t) - 2 e^{- 4 t}

Solution steps

L^{- 1} {\frac{s + 2}{s + 4}}

Take the partial fraction of

\frac{s + 2}{s + 4} : 1 - \frac{2}{s + 4}

= L^{- 1} {1 - \frac{2}{s + 4}}

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 + 4}}

L^{- 1} {1} : δ (t)

L^{- 1} {\frac{2}{s + 4}} : 2 e^{- 4 t}

= δ (t) - 2 e^{- 4 t}

\frac{\partial}{\partial y} (x^{4 y})

x \to - \infty lim (\frac{( 5 x ^{2} - 2 )}{x + 3})

y = x^{2} - 8, y = 7 - 2 x

x \to 0 lim (\frac{∣ x - 1 ∣ - 1}{x})

x \to 0 + lim (a x^{x^{2}})

What is inverse oflaplace (s+2)/(s+4) ?
The answer to inverse oflaplace (s+2)/(s+4) is \delta(t)-2e^{-4t}