calculate expectation of product of two correlated random variable

Question

Problem is like this: $x$ , $y$ are random variables and $x$ is correlated with $y$(specifically, the distribution of $y$ is depend on $x$). $x$ ~ Binomial(m,p), $y$ can be zero or positive integer and there is no additional assumption about distribution of $y$. What i want to show is E[$\frac{\sum_{i=1}^n x_i}{mn-\sum_{i=1}^n y_i}$] > E[$\frac{\sum_{i=1}^n x_i}{mn}$] where n is number of $x_i$'s. It seems obvious that it is true but i'm not sure. How can i show that it is always true? Thanks.