SOLUTION: The sum of the reciprocals of two consecutive odd integers is 8/15. Find the integers. I know the answer is 3 and 5 but I'm not sure how to set up the equation to get there.

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Question 971332: The sum of the reciprocals of two consecutive odd integers is 8/15. Find the integers.
I know the answer is 3 and 5 but I'm not sure how to set up the equation to get there. Thank you!
Found 2 solutions by Alan3354, josgarithmetic:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
1/x + 1/(x+2) = 8/15
--> 3 & 5

Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Put the description into the form of an equation. You literally make what the description says.

n, some number, an integer, or better, a counting number.
2n+1 and 2n+3 are two consecutive ODD integers.

1%2F%282n%2B1%29%2B1%2F%282n%2B3%29=8%2F15
and then a bit of arithmetic.