when the reciprocal of the larger of the two consecutive even integers is subtracted from 4 times the reciprocal of the smaller, the result is 5/6. find integers.

Answer 1

n , (n+2)

4/n - 1/(n+2) = 5/6

24/n - 6/(n+2) = 5

24(n+2) - 6 n = 5n(n+2)

24 n + 48 - 6 n = 5 n^2 + 10 n

5 n^2 - 8 n - 48 = 0

(5 n + 12)(n-4)

so n = 4
n+2 = 6