Let first number be x ; its reciprocal: 1/x
Second number x + 1; its reciprocal: 1
x + 1
Equation:
1/x + 1/(x+1) = 5/6
1(x)(x+1)(6) + 1 (x) (x+1)(6) = 5 (x) (x+1) (6)
x x + 1 6
6 (x + 1) + 6 (x) = 5x (x+1)
6x + 6 + 6x = 5x² + 5x
Equate to zero:
5x² - 6x - 6x + 5x - 6 = 0
5x² - 7x - 6 = 0
(x + 3/5) = 0 (x - 2) = 0
x = -3/5 x = 2
Choose 2 because we're looking for two consecutive positive integers.
The numbers are:
first number: x = 2
second number: x + 1 = 2 + 1 = 3
The two consecutive positive numbers are 2 and 3.
To check:
1/2 + 1/3 = 5/6
3 + 2 = 5/6
6
5/6 = 5/6
NOTE: Keep practicing.