How do i reduce this expression of binomial coefficients

I was solving a problem and am stuck with this expression. Any leads on how can I simplify this expression?

$$\frac{{\sum\limits_{x=Q}^{N-P+Q} (x-Q) \binom{x}{Q} \binom{N-x}{P-Q}}}{{\sum\limits_{x=Q}^{N-P+Q} \binom{x}{Q} \binom{N-x}{P-Q}}}$$

UPDATE: I realized a mistake. expression updated.

Answer

There is a variation of the Vandermonde identity that reads, for $k,m,n\in\mathbf N$:
$$\sum_{i=0}^k\binom im\binom{k-i}n=\binom{k+1}{m+n+1}.$$
Here is how you can remember it: let $0\leq a_0<\cdots

One can restrict the range of $i$ to the values $m\leq i\leq k-n$, as other terms contribute $0$.

So your expression simplfies to
$$\frac{{\sum\limits_{x=Q}^{N-P+Q} \binom{x-1}{Q} \binom{N-x}{P-Q}}}{{\sum\limits_{x=Q}^{N-P+Q} \binom{x}{Q} \binom{N-x}{P-Q}}}= \frac{\binom{N}{P+1}}{\binom{N+1}{P+1}}=\frac{N-P}{N+1}.$$