Is the result of dividing two expected values, a new expected value? In fact, in the probability theory, if $\mathbb{E}_1$ and $\mathbb{E}_2$ are two expected values, then is $\frac{\mathbb{E}_1}{\mathbb{E}_2}$ a new expected value?
I want to know, in general, is the expected value of the ratio of two random variables, the ratio of the expected values?