Question: $\cfrac{-2}{(2x-1)}$?

I want to see if I'm not forgetting reciprocals. And that I'm correct and not misremembering.

It's the negative in front of the parentheses that's throwing me off.

Answer: 
The definition of reciprocal is, "the reciprocal of a number $ u $ is a number $ v $ with the property that $ u \cdot v = 1 $." So if $ u = \frac{-(2x-1)}{2} $, then does your proposed $ v = \frac{-2}{2x-1} $ satisfy this definition? Try multiplying it out and decide for yourself if it does.
The reciprocal of a fraction is simply found by swapping the denominator with the numerator, and also by swapping the numerator for the denominator.
eg the reciprocal of  

$$\frac{a}{b}=\frac{b}{a}$$