[EQ]
\begin{align}
\frac{1}{(1-x)^2} + \frac{2x}{(1-x)^3} &= \sum_{n=0}^\infty n^2x^{n-1}\\
&\Leftrightarrow\\
\frac{1-x}{(1-x)^3} + \frac{2x}{(1-x)^3} &= \sum_{n=0}^\infty n^2x^{n-1}\\
&\Leftrightarrow\\
\frac{1+x}{(1-x)^3} &= \sum_{n=0}^\infty n^2x^{n-1}
\end{align}
[/EQ]