SOLUTION: Simplify the following: a.) (n+2)! ----------- --------- (n+1) (n-1)! b.) 10! ----------- ------- 4! 7!

Algebra ->  Permutations -> SOLUTION: Simplify the following: a.) (n+2)! ----------- --------- (n+1) (n-1)! b.) 10! ----------- ------- 4! 7!      Log On


   

Question 1127579: Simplify the following:
a.) (n+2)!
---------------------
(n+1) (n-1)!
b.) 10!
-------------------
4! 7!
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
a.)
%28n%2B2%29%21%2F%28%28n%2B1%29+%28n-1%29%21%29

.........................n | 1 | 2 | 3 | 4 |+5
%28%28n+%2B+2%29%21%29%2F%28%28n+%2B+1%29+%28n+-+1%29%21%29 | 3 |+8 | 15 | 24 | 35
rule:
1| 3 -> difference is 2: n%2B2=1%2B2=3
2 |+8-> difference is 6: second term->n=2->n%28n%2B2%29=2%282%2B2%29=8
then we conclude:
%28n%2B2%29%21%2F%28%28n%2B1%29+%28n-1%29%21%29=n+%28n+%2B+2%29

b.)


Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


a. Factor the "(n-1)!" out of the numerator and simplify:



b. Factor the 7! out of the numerator and simplify: