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A fraction has a value 2/3. If 4 is added to the numerator and the denominator is decreased by 2, the resulting fractions have the value 6/7. What is the original fraction? (Let x be the numerator and y be the denominator)

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  1. numerator --- x
    denominator --- y

    x/y = 2/3
    2y = 3x
    y = 3x/2

    new fraction:
    (x+4)/(y-2) = 6/7
    6y - 12 = 7x + 28
    6y = 7x + 40
    3(2y) = 7x+40
    3(3x) = 7x + 40
    2x = 40
    x = 20
    y = 30

    the non-reduced fraction was 20/30

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