Question

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

Answer 1

`1/(n^2-n)`

Explanation:

What is `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)`