SOLUTION: there are two positive numbers. the second number is 6 less than the first number. when the reciprocal of the second number is subtracted from the reciprocal of the first the diffe

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Question 602725: there are two positive numbers. the second number is 6 less than the first number. when the reciprocal of the second number is subtracted from the reciprocal of the first the difference is -3/8 FIND THE ANSWER PLEASE
Answer by stanbon(75887) About Me  (Show Source):
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there are two positive numbers. the second number is 6 less than the first number. when the reciprocal of the second number is subtracted from the reciprocal of the first the difference is -3/8
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1st number: x
2nd number: x-6
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Equation:
(1/x) - (1/(x-6)) = -3/8
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Multiply thru by 8x(x-6) to get:
8(x-6) - 8x = -3x(x-6)
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8x-48 - 8x = -3x^2+18x
3x^2 -18x -48 = 0
x^2-6x-16 = 0
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Factor:
(x-8)(x+2) = 0
Positive solutions:
x = 8
x-6 = 2
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Cheers,
Stan H.