SOLUTION: The sum of the reciprocals of 2 consecutive odd integers is 16/63. Find the numbers. I was thinking that the equation was 1/x + 1/x+2= 16/63 Not sure if this is correct. Ple

Question 762740: The sum of the reciprocals of 2 consecutive odd integers is 16/63. Find the numbers.
I was thinking that the equation was 1/x + 1/x+2= 16/63
Not sure if this is correct.
Please help.
Found 2 solutions by josgarithmetic, stanbon:
Answer by josgarithmetic(39627) (Show Source): You can put this solution on YOUR website!
Consecutive ODD numbers, and .
Without the factor 2, each of the numbers may be either odd or even.

NOW, and you can solve according to number properties which you have been studying. Start by multiplying lefthand and righthand members by the LCD, which is .
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The sum of the reciprocals of 2 consecutive odd integers is 16/63. Find the numbers.
I was thinking that the equation was 1/x + 1/x+2= 16/63
----
1st odd number: x-1
2nd odd number: x+1
-----
1/(x-1) + 1/(x+1) = 16/63
------
Multiply thru by 63(x-1)(x+1) to get:
63(x+1) + 63(x-1) = 16(x^2-1)
------------------------------------
126x = 16x^2 - 16
16x^2 - 126x - 16 = 0
----
8x^2 - 63x - 8 = 0
(x-8)(8x+1) = 0
----
Whole number solution:
x = 8
====
1st odd number: 2x-1 = 15
2nd odd number: 2x+1 = 17
==============================
Cheers,
Stan H.
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