Show that for nonnegative integers $m$ and $n$, $\frac{\dbinom{m}{0}}{n+1}-\frac{\dbinom{m}{1}}{n+2}+...+(-1)^m\frac{\dbinom{m}{m}}{n+m+1}$ $=\frac{\dbinom{n}{0}}{m+1}-\frac{\dbinom{n}{1}}{m+2}+...+(-1)^n\frac{\dbinom{n}{n}}{m+n+1}$.
Problem
Source: MOP 2005 Homework - Blue Group #12
Tags: function, integration, calculus, algebra, binomial theorem, algebra unsolved