Given $x,y,n\in\mathbb{N}^+$, and $x<y$, which quantity among
$$ p=\frac{\binom{x+n-1}{n}}{\binom{y+n-1}{n}}\,\,\,\text{ and }\,\,\,q=\frac{\binom{n+1}{n-1}}{\binom{n+2}{n}} $$
is greater?
I tried to use the technique presented in this post Compare ratios of dispositions and combinations, but without success.
I apologize in case it is a trivial question. Thanks however for your help!