Simplify $\frac{n!}{(n + 1)!} - \frac{(n - 1)!}{n!}$ $(n!)/((n+1)!)-((n-1)!)/(n!)$ ?

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Simplify $\frac{n!}{(n + 1)!} - \frac{(n - 1)!}{n!}$ $(n!)/((n+1)!)-((n-1)!)/(n!)$ ?

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Answer 1 · 2017-11-30T09:42:51

$\frac{1}{n^{2} - n}$ $1/(n^2-n)$

Explanation:

What is $n!$ $n!$ ( $n$ $n$ factorial ) ?

$n! =1xx2xx3xx...xxn$

So,

$(n!)/((n+1)!)-((n-1)!)/(n!)$
$=cancel(1xx2xx...xxn)/(cancel(1xx2xx...xxn)xx(n+1))-cancel(1xx2xx...xx(n-1))/(cancel(1xx2xx...xx(n-1))xxn)$
$=1/(n+1)-1/n$
$=(n-(n+1))/((n+1)(n))$
$=-1/(n^2+n)$

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Simplify $\frac{n!}{(n + 1)!} - \frac{(n - 1)!}{n!}$ $(n!)/((n+1)!)-((n-1)!)/(n!)$ ?

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Explanation:

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Simplify (n!)/((n+1)!)-((n-1)!)/(n!)n!(n+1)!−(n−1)!n!(n!)/((n+1)!)-((n-1)!)/(n!)?

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Simplify $\frac{n!}{(n + 1)!} - \frac{(n - 1)!}{n!}$ $(n!)/((n+1)!)-((n-1)!)/(n!)$ ?