Answer
See below.
Work Step by Step
By definition, we have:
$LHS=\binom n {r+1}=\frac{n!}{(n-r-1)!(r+1)!}$
$RHS=\frac{n-r}{r+1}\binom n {r}=\frac{n-r}{r+1}\times\frac{n!}{(n-r)!(r)!}=\frac{n!}{(n-r-1)!(r+1)!}=LHS$
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