Given two random variables, $V \sim \beta^{'}(P,PM)$ and $U \sim \Gamma(PM,\zeta)$, where $\beta^{'}$ is the Beta-Prime distribution, $\Gamma$ is the Gamma distribution and $\zeta$ is a real constant value.
What would be the result of the following expectation?
$$E \left[ \frac{V}{U} \right] = ?$$