Is the reciprocal of $\cfrac {-(2x-1)}{2}$ $\cfrac{-2}{(2x-1)}$?
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.
The definition of reciprocal is, &quot;the reciprocal of a number $ u $ is a number $ v $ with the property that $ u \cdot v = 1 $.&quot;  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
$$\frac{a}{b}=\frac{b}{a}$$