SOLUTION: The sum of the reciprocals of two consecutive integers is 5/6. Find two integers

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Question 371942: The sum of the reciprocals of two consecutive integers is 5/6. Find two integers
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
N and N%2B1 are the integers.
1%2FN%2B1%2F%28N%2B1%29=5%2F6
Use the common denominator, 6N%28N%2B1%29

%286%28N%2B1%29%2B%286N%29-5N%28N%2B1%29%29%2F%286N%28N%2B1%29%29=0
%286N%2B6%2B6N-5N%5E2-5N%29%2F%286N%28N%2B1%29%29=0
%28-5N%5E2%2B7N%2B6%29%2F%286N%28N%2B1%29%29=0
Factor the numerator.
%28%285N%2B3%29%28-N%2B2%29%29%2F%286N%28N%2B1%29%29=0
Two solutions but only one is an integer solution.
-N%2B2=0
N=2
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.
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2 and 3 are the integers.