Binomial Distribution formula

Question

If $X\sim B(n,p)$, show that $P(X=r+1)=P(X=r) \cdot \frac{p(n-r)}{q(r+1)}$ for $r=0,1,...,n-1$

My attempt,

$P(X=r+1)={_n}C_{r+1}(p)^{r+1}(1-p)^{n-(r+1)}$

How to proceed then?

Answer 1

$${ n \choose r+1} = \frac{n-r}{n + 1} {n \choose r}$$