Cant understand this transition

[nhrock3]

http://i50.tinypic.com/2a6w9qg.jpg

cant see how they put the only the denominator to be equal the new expression.
?

 

[vela]

They used

$$\frac{1}{1-x}=1+x+x^2+x^3+...$$

where $x=2z^2/4!+...$. It looks like they made a sign mistake when they did that, though.