$(3$ points$)$ A dynamic system has the following equation of motion $x^{}(t)+3x^{}(t)+2x^{}(t)-3^{\text{'}}=2f(t),$ where $x$ is the output of the system, and $f$ is the input. Determine the transfer function $G(s)=\frac{x(s)}{F(s)}$ of the given dynamic system, assuming zero initial conditions.

$(4$ points$)$ Write the partial fraction expansion of the following transfer function; WRITE OLY THE PARTIAL FRACTION EXPANSION; YOU DON'T NEED TO SOLVE IT USING INVERSE LAPLACE TRANSFORM.

$G(s)=\frac{s+3}{s^3+7s^2+10s}$

Solve $1$ and $2$ in details please