How Do You Simplify Algebraic Fractions from Red to Blue Box?

[ledhead86]

Apparently I've forgotten how to simplify algebraic fractions. I included the problem as a picture.
http://community.webshots.com/photo/461491683/476214616XrKOZJ#"
I can't figure out how they went from the red box and then to the green box and then the blue box. Obviously, I understand from the green to purple, but the rest is puzzling me. Any help would be appreciated.

 

[ledhead86]

sorry, fixed the pic

 

[mezarashi]

From red to green, they did this:

$$\frac{2}{2+h} -1 = \frac{2}{2+h} - 1\frac{(2+h)}{(2+h)} = \frac{2}{2+h} - \frac{2+h}{2+h}$$

Multiplying by fractions in the form of b/b is equal to multiplication by 1.

From purple to blue:

$$\frac{\frac{-h}{2+h}}{h} = \frac{-h}{h(2+h)}$$

They just divided the top part by h, the same way you would do: $$\frac{\frac{1}{3}}{2} = \frac{1}{3\times2}$$