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

Algebra ->  Rational-functions -> 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      Log On


   

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(39625) About Me  (Show Source):
You can put this solution on YOUR website!
Consecutive ODD numbers, 2x%2B1 and 2x%2B3.
Without the factor 2, each of the numbers may be either odd or even.

NOW, 1%2F%282x%2B1%29%2B1%2F%282x%2B3%29=16%2F63 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 63%282x%2B1%29%282x%2B3%29.

Answer by stanbon(75887) About Me  (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
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1st odd number: x-1
2nd odd number: x+1
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1/(x-1) + 1/(x+1) = 16/63
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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
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Whole number solution:
x = 8
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1st odd number: 2x-1 = 15
2nd odd number: 2x+1 = 17
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Cheers,
Stan H.