SOLUTION: the sum of the reciprocals of two consecutive even integers is 10 times the reciprocal of their product. find these integers.

Question 472731: the sum of the reciprocals of two consecutive even integers is 10 times the reciprocal of their product. find these integers.
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
Let n and n+2 be the two consecutive even integers.
So we can write
1/n + 1/(n+2) = 10/(n(n+2))
The LCD of the LHS is n(n+2)
Since denominators are equal we can set the numerators equal:
(n+2) + n = 10
2n + 2 = 10
This gives n = 4
So the integers are 4 and 6
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