calculus - Proof that ${nchoose r}$ always yields a natural number proof by induction

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Hi I'm trying to prove that the ${n\choose r}$ formula gives a natural number by using proof by induction and I'm stuck on the last stage (in the picture above). Have I messed up earlier on and if not then how can I show that $\frac{n+1}{n-r+1}$ is a natural number. I know there are other articles but I can't seem to find an answer to this.
Cheers