Answer:

x = smaller integer

x+1 = larger integer

Then, 1/x + 1/(x+1) = 13/42

Multiply both sides by the LCD, 42x(x+1)

Then, 42(x+1) + 42x = 13x(x+1)

Simplifying, we have 84x + 42 = 13x2 + 13x

13x2 - 71x - 42 = 0

(13x + 7)(x - 6) = 0

x = -7/13 or 6

The integers are 6 and 7.

Step-by-step explanation:

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