What is inverse oflaplace ((s-2))/((s-3)(s+1)) ?

The answer to inverse oflaplace ((s-2))/((s-3)(s+1)) is 1/4 e^{3t}+3/4 e^{-t}

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inverse oflaplace ((s-2))/((s-3)(s+1))

inverse laplace

\frac{( s - 2 )}{( s - 3 ) ( s + 1 )}

\frac{1}{4} e^{3 t} + \frac{3}{4} e^{- t}

Solution steps

L^{- 1} {\frac{( s - 2 )}{( s - 3 ) ( s + 1 )}}

Take the partial fraction of

\frac{s - 2}{( s - 3 ) ( s + 1 )} : \frac{1}{4 ( s - 3 )} + \frac{3}{4 ( s + 1 )}

= L^{- 1} {\frac{1}{4 ( s - 3 )} + \frac{3}{4 ( s + 1 )}}

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} {\frac{1}{4 ( s - 3 )}} + L^{- 1} {\frac{3}{4 ( s + 1 )}}

L^{- 1} {\frac{1}{4 ( s - 3 )}} : \frac{1}{4} e^{3 t}

L^{- 1} {\frac{3}{4 ( s + 1 )}} : \frac{3}{4} e^{- t}

= \frac{1}{4} e^{3 t} + \frac{3}{4} e^{- t}

\int \frac{sin ^{7} ( 4 x )}{cos ^{4} ( 4 x )} d x

x \to 0 lim (\frac{sin ( 11 x )}{x})

(arcsin (x))^{e^{- x}}

lo g_{5} (sin (x))

\int_{\frac{1}{5}}^{3} 4 x ln (5 x) d x

What is inverse oflaplace ((s-2))/((s-3)(s+1)) ?
The answer to inverse oflaplace ((s-2))/((s-3)(s+1)) is 1/4 e^{3t}+3/4 e^{-t}