Explain how to use convolution along with the formula \(\mathcal{L}\{e^{at})=\frac{1}{s-a}\)to find the following inverse Laplace transform:
\[ \mathcal{L}^{-1}\left\{ \frac{5}{3 \, {\left(s + 4\right)} {\left(s - 6\right)}} \right\} \]
Answer:
\[ \frac{1}{6} \, e^{\left(6 \, t\right)} - \frac{1}{6} \, e^{\left(-4 \, t\right)} \]