Simplifying $\frac{1}{x^4+4x^2}$ I'm trying to solve this problem on my own and it involves simplifying the expression in the title.
In the solutions it says it's this:
$$\frac{1}{x^4+4x^2} = \frac{1}{4}\Biggl[\frac{1}{x^2}-\frac{1}{x^2+4}\Biggr]$$
But I can't for the life of me figure out where the 1/4 came from. Or exactly how they got to this answer...

We can write the fraction as,
$$\frac{1}{x^4 +4x^2} = \frac{1}{4}\cdot \frac{4}{x^2(x^2+4)}$$
The fraction $\frac{4}{x^2(x^2+4)}$ can be written as..
\begin{align}
\frac{1}{4}\cdot \frac{4}{x^2(x^2+4)}=\frac{1}{4}\Biggl[\frac{(x^2+4)-x^2}{x^2(x^2+4)}\Biggr]\\
=\frac{1}{4}\Biggl[\frac{1}{x^2}-\frac{1}{x^2+4}\Biggr]
\end{align}
Understand?
