How can I force this expression into a given form? This problem has been irritating me, and conceptually, it should be very straight forward! This equation is derived from a circuit with a dependent voltage source; it describes the gain.
$ G(\omega)=\huge\frac{\mu}{1+\frac{R_0}{R_L}}\frac{\frac{R_i}{1+j\omega C_iR_i}}{R_s+\frac{R_i}{1+j\omega C_iR_i}}$
Here's the goal: Express this equation on the form of
$G(\omega)=K\large\frac{1}{1+j\beta \omega}$
where $K$ and $\beta$ are simply variable representations of some expression - this is just a general form or "wrapper" if you will. 
It is obvious that the first fraction in the first expression will be contained in $K$. The simplification will therefore be applied to the second fraction. The problem that I encounter is in regard to $\large R_s$. My first inclination is to multiply the numerator and denominator by
$\large \frac{1+j\omega C_iR_i}{R_i}$. 
When I do, I am left with
$G(\omega)=K\LARGE\frac{1}{\frac{R_s}{R_i}+j\omega C_iR_s+1}$
Now I have three terms on the bottom - close, but not of the proper form. There probably is a very simple solution that I am missing for some reason. Any constructive input is appreciated. 
NOTE: $j$ is the same as $i$ - an imaginary number.
 A: You can rewrite the denominator of your last expression as $(1+R_s/R_i) + j\omega C_iR_s$, which is a constant times $1 + j\omega (C_iR_s/(1+R_s/R_i))$.
A: $\newcommand{\+}{^{\dagger}}%
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$$
K = G\pars{0} = {\mu \over 1 + R_{0}/R_{L}}\,{R_{i} \over R_{s} + R_{i}}
\quad\imp\quad
G\pars{\omega}
=
K\,{R_{s} + R_{i} \over R_{i}}\,
{R_{i} \over R_{s} + R_{i} + jR_{s}C_{i}R_{i}\omega}
$$
$$
G\pars{\omega}
=
K\pars{R_{s} + R_{i}}\,
{1 \over R_{s} + R_{i} + jR_{s}C_{i}R_{i}\omega}
=
K\,
{1 \over 1 + j\bracks{R_{s}C_{i}R_{i}/\pars{R_{s} + R_{i}}}\omega}
$$
\begin{align}\vphantom{\Huge A}&\end{align}
$${\large%
G\pars{\omega}
=
{K \over 1 + j\beta \omega}\,,
\qquad
K \equiv {\mu \over 1 + R_{0}/R_{L}}\,{R_{i} \over R_{s} + R_{i}}\,,\qquad
\beta \equiv {R_{s}C_{i}R_{i} \over R_{s} + R_{i}}}
$$
