I've been searching the answer to my question (https://stats.stackexchange.com/questions/476156/how-to-estimate-the-correlation-between-ratio-and-ratios-denominator) and think that it might be formulated like this as well. Is there an answer?
Greatful for any help!
For any two random variables $Z,W$, we have $$\operatorname{Cov}(Z,W)=\operatorname{E}[ZW]-\operatorname{E}[Z]\operatorname{E}[W].$$
Therefore,
$$\operatorname{Cov}\left({\frac{X}{Y},Y}\right)=\operatorname{E}[X]-\operatorname{E}[X/Y]E[Y]$$