SOLUTION: The sum of the reciprocals of 2 consecutive odd integers is 8/15. Find the numbers.

Question 1156497: The sum of the reciprocals of 2 consecutive odd integers is 8/15. Find the numbers.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
3 and 5
-
numbers x and x+2;

.

.
,

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The fraction result does not work for the problem description.
Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!
The sum of the reciprocals of 2 consecutive odd integers is 8/15. Find the numbers.

Let the smaller odd integer be N
Then the larger odd integer = N + 2
We then get:
15(N + 2) + 15N, "=", 8N(N + 2) ------ Multiplying by LCD, 15N(N + 2)

------ Replacing - 7N with - 12N + 5N
4N(N - 3) + 5(N - 3) = 0
(N - 3)(4N + 5) = 0
N, or smaller odd integer = or
Do you know what the larger odd integer is now?
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