The following transfer functions do not share a common denominator polynomial, but they may be made to do so by multiplying their numerators and denominators by appropriate factors. Obtain simulation diagram involving only three integrators. Then obtain state space model in matrix form.

\[
\begin{aligned}
& \mathrm{T}_{11}(s)=\frac{\mathrm{Y}_{1}(s)}{\mathrm{U}_{1}(s)}=\frac{3 s+1}{(s+2)(s+3)} \\
& \mathrm{T}_{21}(s)=\frac{\mathrm{Y}_{2}(s)}{\mathrm{U}_{1}(s)}=\frac{16 s}{(s+1)(s+3)}
\end{aligned}
\]