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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 -

    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

  • precal help -

    the denominator of a fraction is 1 more than the numerator.the sum of the fraction and its reciprocal is 2 1/30.find the fraction

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