We want to approximate a fourth-order system by a lower-order model. The transfer function of the original system is
$$
\begin{aligned}
H(s) & =\frac{s^3+7 s^2+24 s+24}{s^4+10 s^3+35 s^2+50 s+24} \\
& =\frac{s^3+7 s^2+24 s+24}{(s+1)(s+2)(s+3)(s+4)} .
\end{aligned}
$$
Show that if we obtain a second-order model by the method of Section 5.8 , and we do not specify the poles and the zero of $L(s)$, we have
$$
\begin{aligned}
L(s) & =\frac{0.2917 s+1}{0.399 s^2+1.375 s+1} \\
& =\frac{0.731(s+3.428)}{(s+1.043)(s+2.4)} .
\end{aligned}
$$