How do I get from $\frac{-x+1}{-x+2}$ to $1 + \frac{1}{x-2}$ wolframalpha tells me it's the same but I can not follow how to get from one to another. 
$$\frac{-x+1}{-x+2} =  \frac{1-x}{2-x} = \>? \dots$$
I don't get any further, always end up where I started.

$$\begin{align} \dfrac{1-x}{2-x} & = \dfrac{-(x - 1)}{-(x-2)} \\ \\ &= \dfrac{x-1}{x-2} \\ \\ &= \dfrac {x-1 \color{blue}{\bf - 1 + 1}}{x-2} \\ \\ & = \dfrac{(x-2) +1}{x - 2}\\ \\ & = \dfrac{x-2}{x-2} + \dfrac 1{x-2}\\ \\ & = 1 + \frac{1}{x - 2}\end{align}$$
