Use partial fractions to find the inverse Laplace transform of the following function.
\[
F(s)=\frac{4-5 s}{s^{2}+11 s+28}
\]
Elick the icon to view the table of Laplace transforms.
\[
\mathscr{L}^{-1}\{\mathrm{~F}(\mathrm{~s})\}=
\]
(Type an expression using $t$ as the variable.)

Step 1 ：First, decompose the function into partial fractions. The denominator of the function can be factored as \((s+4)(s+7)\). So, we can write the function as a sum of two fractions, each with one of these factors in the denominator.

Step 2 ：\[F(s) = \frac{4 - 5s}{s^2 + 11s + 28} = \frac{-13}{s + 7} + \frac{8}{s + 4}\]

Step 3 ：Now that we have decomposed the function into partial fractions, we can use the table of Laplace transforms to find the inverse Laplace transform of each fraction. The inverse Laplace transform of \(\frac{1}{s+a}\) is \(e^{-at}\).

Step 4 ：\[\mathscr{L}^{-1}\{F(s)\} = 8e^{-4t} - 13e^{-7t}\]

Step 5 ：Final Answer: The inverse Laplace transform of the function \(F(s)=\frac{4-5 s}{s^{2}+11 s+28}\) is \(\boxed{8e^{-4t} - 13e^{-7t}}\).