Simplifying Integrands: How to Factor Out Constants in the Denominator?

[ohms law]

This equality is given in an example, in my textbook:

$\int\frac{1}{a^2+x^2}dx=\frac{1}{a^2}\int\frac{1}{1+(\frac{x}{a})^2}dx$

So, my question is simply... how?
This is really more of an algebra question, but it'd really help me to see some more detail here.

 

[The Dragonfly]

$\frac{1}{a^2+x^2} = \frac{1}{a^2(1+ \frac{x^2}{a^2})} = \frac{1}{a^2}\frac{1}{1+ (\frac{x}{a})^2}$

 

[ohms law]

I see that... sort of. It's a form of factoring, obviously.
I don't quite get the $\frac{x^2}{a^2}$ bit, though...
Well, wait: $a^2\times1=a^2$ obviously, and $a^2\times\frac{x^2}{a^2}=x^2$ right? Neat trick, there. Completely obvious too, now that I think about it, but... I guess that I just didn't realize that could be done. Weird.

 

[iRaid]

Just think of it as factoring out an a² from the bottom. Here's an easier example:
$$\frac{1}{4+x^{2}}=\frac{1}{(4)1+\frac{x^{2}}{4}}=(\frac{1}{4})\frac{1}{1+{\frac{x^{2}}{4}}}$$