The only thing I can say is that the transfer function is the ratio between the output and the input in a system. This mean if you call $\rho$ the conductance and $x$ the concentration, you have: $$H(s)=\frac{\rho(s)}{x(s)}$$ So you get: $$H(s)=\frac{As+AC+BCx}{xs(s+C)}$$ considering you did the Laplace transform respect to the time $t$. If you have an input $x(t)$, your output will be: $$\rho(s)=H(s)x(s)$$