SOLUTION: The sum of the reciprocals of two consecutive odd integers is 16 times the reciprocal of their product. Find these integers.

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Question 151173: The sum of the reciprocals of two consecutive odd integers is 16 times the reciprocal of their product. Find these integers.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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The sum of the reciprocals of two consecutive odd integers is 16 times the reciprocal of their products. Find these integer.
:
Two consecutive odd integers: x, (x+2)
:
write an equation for following statement
"The sum of the reciprocals of two consecutive odd integers is 16 times the reciprocal of their product."
1%2Fx + 1%2F%28%28x%2B2%29%29 = 16(1%2F%28x%28x%2B2%29%29)
:
1%2Fx + 1%2F%28%28x%2B2%29%29 = 16%2F%28x%28x%2B2%29%29
Multiply equation by x(x+2)
:
(x+2) + x = 16
;
2x = 16 - 2
x = 14%2F2
x = 7 & 9 are the two consecutive odd integers
;
:
Check solution in original equation:
1%2F7 + 1%2F9 = 16(1%2F%287%2A9%29)
1%2F7 + 1%2F9 = 16%2F63
9%2F63 + 7%2F63 = 16%2F63