# Cancel fractions

Compress the expression of factorial:

(n+6)!/(n+4)!-n!/(n-2)!

Result

e = (Correct answer is: 12n+30)

#### Solution:

$e=(n+6)! / (n+4)! -n!/ (n-2)! \ \\ e=(n+6)(n+5) (n+4)! / (n+4)! -n(n-1) (n-2)! / (n-2)! \ \\ e=(n+6)(n+5)-n(n-1) \ \\ e=n^2 +6n+5n+6 \cdot \ 5 -n^2-n \ \\ e=12n+30$

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