I can't see how these two expressions are equal,

$\displaystyle \frac{ \frac{1}{2} }{3 - \left[ - (x-2) \right]} = \frac{1}{3} \left[ \frac{ \frac{1}{6} }{1 - \left[ -\frac{ (x-2) }{3} \right] \right]$

I can see them pulling out a 3 of the bottom, but why is the top being multipled by, 1\3?

I took a factor of 3 out of the denominator now why do I have to change the top number to do so?

Can someone explain to me what I'm missing?