Question 712196
The sum of the reciprocals of two consecutive positive integers is seventeen/seventy-two. Write an equation that can be used to find the two integers. What are the integers? 
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First from "two consecutive positive integers" we can create our variables:
Let x = smaller of two consecutive integers
then
x+1 = larger of two consecutive integers
.
Reciprocal of x is
1/x
Reciprocal of x+1 is
1/(x+1)
.
From: "The sum of the reciprocals of two consecutive positive integers is seventeen/seventy-two." we get our equation:
1/x + 1/(x+1) = 17/72
To solve, multiply both sides by 72x(x+1) to get:
72(x+1) + 72x = 17(x(x+1))
Can you finish from here?