Explain how to use convolution along with the formula \(\mathcal{L}\{e^{at})=\frac{1}{s-a}\)to find the following inverse Laplace transform:

\[ \mathcal{L}^{-1}\left\{ \frac{7}{3 \, {\left(s - 5\right)} {\left(s - 6\right)}} \right\} \]

Answer:

\[ \frac{7}{3} \, e^{\left(6 \, t\right)} - \frac{7}{3} \, e^{\left(5 \, t\right)} \]