SOLUTION: the denominator of a fraction is 2 more than the numerator. the sum of the fraction and its reciprocal is 34/15. find the fraction.

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Question 84634: the denominator of a fraction is 2 more than the numerator. the sum of the fraction and its reciprocal is 34/15. find the fraction.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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the denominator of a fraction is 2 more than the numerator. the sum of the fraction and its reciprocal is 34/15. find the fraction.
:
Let x = the numerator, then (x+2) = the denominator
:
x%2F%28%28x%2B2%29%29 + %28%28x%2B2%29%29%2Fx = 34%2F15
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Multiply equation by 15x(x+2) and you have:
15x(x) + 15(x+2)(x+2) = 34x(x+2)
:
15x^2 + 15(x^2 + 4x + 4) = 34x^2 + 68x
:
15x^2 + 15x^2 + 60x + 60 = 34x^2 + 68x
:
30x^2 + 60x + 60 = 34x^2 + 68x
:
0 = 34x^2 - 30x^2 - 60x + 68x - 60
:
0 = 4x^2 + 8x - 60
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Simplify, divide by 4
x^2 + 2x - 15 = 0
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Factors to:
(x + 5)(x - 3) = 0
:
x = -5: the fraction is 5/3
and
x = + 3; the fraction is 3/5
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