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A denominator of a fraction exceeds the numerator by 1 if 2 is taken from each the sum of the reciprocal of the new fraction and 4 times the original fraction is 5. Find the original fraction

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  1. original fraction ---- x/(x+1)

    new fraction = (x-2)/(x-1)

    (x-1)/(x-2) + 4x/(x+1) = 5
    times (x-2)(x+1), the LCD

    (x-1)(x+1) + 4x(x-2) = 5(x-2)(x+1)
    x^2 - 1 + 4x^2 - 8x = 5x^2 - 5x - 10
    3x - 9 = 0
    x = 3

    original fraction is 3/4

    check:
    new fraction = 1/2
    1/(1/2) + 4(3/4)
    = 2 + 3 = 5 , as needed

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