Negative Reciprocals

Question

What is the negative reciprocal of (-1 + n) / n? I know how to convert simple fractions (such as 1/2) to their negative reciprocals, however, I don't know what to do if there is an extra element (such as adding 1 to the numerator). How would it work?

Answer 1

The reciprocal of $ \frac{-1+n}{n}$ is $ \frac{n}{-1+n}$. Thus, what you are looking for is given by $ \frac{n}{1-n}$.