# SOLUTION: The difference of the reciprocals of two consecutive even integers is 1/12 Find the Integers

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 Question 373161: The difference of the reciprocals of two consecutive even integers is 1/12 Find the IntegersAnswer by CharlesG2(828)   (Show Source): You can put this solution on YOUR website!The difference of the reciprocals of two consecutive even integers is 1/12 Find the Integers let n be one integer let n + 2 be the next consecutive even integer 1/n - 1/(n + 2) = 1/12 12/n - 12/(n + 2) = 1 12 - 12n/(n + 2) = n 12(n + 2) - 12n = n(n + 2) 12n + 24 - 12n = n^2 + 2n 24 = n^2 + 2n 0 = n^2 + 2n - 24 0 = (n - 4)(n + 6) (by FOIL this same, 6n - 4n = 2n) n = 4 or n = -6 check: 1/4 - 1/6 = 1/4 * 3/3 - 1/6 * 2/2 = 3/12 - 2/12 = 1/12, yes 1/(-6) - 1/(-4) = -1/6 + 1/4 = -1/6 * 2/2 + 1/4 * 3/3 = -2/12 + 3/12 = 1/12, yes 4 and 6 or -6 and -4 are answers