Question

(n+1)!-n! \(n-1)!
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Answer 1

[(n+1)!-n!]/(n-1)!=

[n!*(n+1)-n!]/(n-1)!=

n!(n+1-1)/(n-1)!=

(n-1)!*n*n/(n-1)!=n²

Answer 2

$\frac{(n+1)!-n!}{(n-1)!} =\\ \\\\ \\ \frac{(n-1)!*n*(n+1) -(n-1)!*n}{(n-1)!}=\\ \\\\ \\ \frac{(n-1)!*[n*(n+1)-n]}{(n-1)!}=\\ \\ \\ \frac{(n-1)!*(n^{2}+n-n)}{(n-1)!}=\\ \\ \\ \frac{(n-1)!*n^{2}}{(n-1)!}=n^{2}$