We let X be the first integer and X + 1 be the second integer. We write: (1/X) + [1/(X + 1)] = 7/24 --> Multiply (X)(X + 1)(24) to the whole equation to leiminate the denominators: [24X(X + 1)] {(1/X) + [1/(X + 1)] = 7/24} --> [24(X + 1)] + 24X = 7(X)(X + 1) --> 24X + 24 + 24X = 7X^2 + 7X --> 0 = 7X^2 - 41X - 24 --> X = 6.39, -0.536. 1/6.39 and 1/7.39
