Please: simplify (n+3)!-(n+1)!/(n+3)!+(n+1)! ?

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please: simplify (n+3)!-(n+1)!/(n+3)!+(n+1)! ?

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Answer 1 · 2017-10-01T06:26:50

#((n+3)!-(n+1)!)/((n+3)!+(n+1)!)=1-2/(n^2+5n+7)#

#((n+3)!-(n+1)!)/((n+3)!+(n+1)!)#

= #((n+3)xx(n+2)xx(n+1)!-(n+1)!)/((n+3)xx(n+2)xx(n+1)!+(n+1)!)#

= #((n+1)![(n+3)(n+2)-1])/((n+1)![(n+3)(n+2)+1])#

= #((n+3)(n+2)-1)/((n+3)(n+2)+1]#

= #(n^2+5n+6-1)/(n^2+5n+6+1)#

= #(n^2+5n+5)/(n^2+5n+7)#

= #(n^2+5n+7-2)/(n^2+5n+7)#

= #1-2/(n^2+5n+7)#