SOLUTION: (1/n-1)-(1/n)=5/60

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Question 1115211: (1/n-1)-(1/n)=5/60
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
(1/n-1)-(1/n)=5/60
----
If you mean
1/(n-1)-(1/n)=5/60
Multiply by n*(n-1)
n - (n-1) = 5n*(n-1)/60
1 = (5n^2 - 5n)/60
5n^2 - 5n = 60
n^2 - n = 12
Solve for n

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
1%2F%28n-1%29 - 1%2Fn = 5%2F60   ====>


1%2F%28n-1%29 - 1%2Fn = 1%2F12   ====>


n%2F%28n%2A%28n-1%29%29+-+%28n-1%29%2Fn = 1%2F12


1%2F%28n%2A%28n-1%29%29 = 1%2F12    ====>


n*(n-1) = 12    <<<---=== the product of two consecutive integers = 12  ====>


there are 2 solutions:   a) n= 4   and   b) n= -3.