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let numerator be x let denominator be x+2 fraction = x/(x+2) (x+5)/(x+2) = x/(x+2) +1 (x+5)/(x+2) - x/(x+2) =1 (x+5 -x)/(x+2)= 1 5/(x+2) = 1 5 = x+2 5-2 = x x=3 The fraction is 3/5

Let n = numerator then from "denominator of a fraction exceeds the numerator by 2" we have n+2 = denominator . We derive our equation from:"If 5 be added to the numerator the fraction increases by unity": (n+5)/(n+2) = n/(n+2) + 1 multiplying both sides by (n+2) (n+5) = n + (n+2) n+5 = 2n + 2 5 = n + 2 3 = n (numerator) . Denominator: n+2 = 3+2 = 5 . Solution then is numerator/denominator: 3/5