Posted by **Anonymous** on Friday, September 21, 2012 at 4:03am.

The numerator of a fraction is four less than the denominator The sum of the fraction and its reciprocal is 5/2 Find the numerator and denominator if each is a positive integer

- precal help -
**Reiny**, Friday, September 21, 2012 at 8:53am
denominator --- x

numerator ---- x-4

(x/x-4) + (x-4)/x = 5/2

times 2x(x-4)

2x^2 + 2(x-4)^2 = 5x(x-4)

2x^2 + 2x^2 - 16x + 32 = 5x^2 - 20x

-x^2 + 4x + 32 = 0

x^2 -4x - 32 = 0

(x-8)(x+4) = 0

x = 8 or x = -4 , but x was positive

so x = 8

so original fraction was 4/8 or 1/2

check:

1/2 + 2/1 = 2 1/2 = 5/2

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