SOLUTION: If [n/(n-1)] x [1/n] x [n/(n+1)] = 5/k for positive integers n and k, what is the value of k? the answer is 24, but I do not understand how they got this answer. Can you he

Question 466830: If [n/(n-1)] x [1/n] x [n/(n+1)] = 5/k for positive integers n and k, what is the value of k?
the answer is 24, but I do not understand how they got this answer.
Can you help?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
If [n/(n-1)] x [1/n] x [n/(n+1)] = 5/k for positive integers n and k, what is the value of k?
the answer is 24
-----------------------
Cancel any factors common to a numerator and a denominator:
Common factor: n
----------------------
[n/(n-1)] x [1/(n+1)] = 5/k
---
[n/(n^2-1)] = 5/k
---
If you assume the numerators and the denominators
are respectively equal you would get n = 5
and n^2-1 = k
--
Then, if n = 5, n^2-1 would be 24
And you would conclude that k = 24.
----
The only trouble is that n does not have to be 5.
It could be 2*5 = 10
Then the denominator would be 2(n^2-1) = 48
Then k would be 48.
As you can see, many other answers are also possible for "k".
Cheers,
Stan H.
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