The numerator of a positive fraction is 2 less than its denominator. By adding 1½ to the fraction, the fraction is reversed. Find the original fraction.

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2 answers

d - 2 = n ............ (i)
the first sentence (d-2)/d
If 1 1/2 is added it becomes the reversed thus the denominator is 2 less than the numerator
(d - 2)/d + 1 1/2 = (d + 2)/d
Solving the equation d = 3 and n = 1 which is 1/3
[(x-2) / x] + 3/2 = x / (x-2)

2(x-2)^2 + 3x^2 - 6x = 2x^2

2x^2 - 8x + 8 + 3x^2 - 6x = 2x^2 ... 3x^2 - 14x + 8 = 0

there is one positive solution ... 2/4 + 3/2 = 4/2