Understanding a step in a double series proof I'm really confused, how do they get from the first line to the second line ?
$$\begin{align*}
S&=\frac12\left[\sum_{m=1}^\infty\sum_{n=1}^\infty\frac{m^2n}{3^m(n\cdot3^m+m\cdot3^n)}+\sum_{m=1}^\infty\sum_{n=1}^\infty\frac{n^2m}{3^n(n\cdot3^m+m\cdot3^n)}\right]\\\\
&=\frac12\sum_{m=1}^\infty\sum_{n=1}^\infty\frac{mn}{3^{m+n}}
\end{align*}$$
Can anyone explain this step?

Making a common denominator and factoring, observe that:
\begin{align*}
\frac{m^2n}{3^m(n \cdot 3^m + m \cdot 3^n)} + \frac{n^2m}{3^n(n \cdot 3^m + m \cdot 3^n)}
&= \frac{m^2n \cdot 3^n + n^2m \cdot 3^m}{3^m3^n(n \cdot 3^m + m \cdot 3^n)} \\
&= \frac{mn(m \cdot 3^n + n \cdot 3^m)}{3^{m+n}(n \cdot 3^m + m \cdot 3^n)} \\
&= \frac{mn}{3^{m+n}} \\
\end{align*}
