A positive integer is 2 less than another. If the sum of the reciprocal of the smaller and twice the reciprocal of the larger is 5/12, then find the two integers.

Question

algebraic expression is:
1/n-2 + (2)1/n = 5/12

Answer 1

small = s and b = big

s = b-2

1/s + 2/b = 5/12
so
1/(b-2) + 2/b = 5/12 agreed

multiply by 12 b (b-2)

12 b + 24(b-2) = 5 b(b-2)

12 b + 24 b - 48 = 5 b^2 - 10 b

0 = 5 b^2 - 46 b + 48
0 = (b-8)(5b-6)
so use b = 8
s = b-2 = 6