SOLUTION: (2n+1)!/(n+2)! * (n-1)!/(2n-1)!=3/5 what is n?

Algebra ->  Permutations -> SOLUTION: (2n+1)!/(n+2)! * (n-1)!/(2n-1)!=3/5 what is n?      Log On


   

Question 383270: (2n+1)!/(n+2)! * (n-1)!/(2n-1)!=3/5 what is n?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
(2n+1)!/(n+2)! * (n-1)!/(2n-1)!=3/5 what is n?
----------------------
Rearrange so you can see whats happening:
[(2n+1)!/(2n-1)!] = 3/5
----------------------
Cancel factors that are common to a numerator and a denominator:
[(2n+1)(2)/1] = 3/5
=====
[4n+2]/[n^2+3n+2] = 3/5
----
5(4n+2) = 3(n^2+3n+2)
===
20n+10 = 3n^2+9n+6
------
3n^2-11n-4 = 0
------
3n^2-12n+n-4 = 0
Factor:
3n(n-4)+(n-4) = 0
(n-4)(3n+1) = 0
Positive solution:
n = 4
======================
Cheers,
Stan H.