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A fraction's numerator is 3 less than its denominator. Its reciprocal is 4 times its value. It is greater than 0. What is the fraction?

  • math -

    (D-3)/D = fraction=1/4fraction
    fraction^2=1/4
    fraction=1/2
    fraction=3/6

  • math -

    let the denominator be x
    then the numerator is x-3
    and the fraction is (x-3)/x

    the reciprocal is 4 times the original fraction
    ---> x/(x-3) = 4(x-3)/x

    cross-multiplying and simplifying I got
    x^2 - 8x + 12 = 0
    (x-2)(x-6) = 0
    x = 2 or x = 6
    but x=2 produces a negative value, which was not allowed
    so x = 6

    so the fraction was 3/6 = 1/2

    reciprocal is 2/1 = 2
    is that 4(1/2) ? yes!

  • math -

    Can you help me with a math problem

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