SOLUTION: find two consecuive positive integers if the difference of their reciprocals is 1/12

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Question 146233: find two consecuive positive integers if the difference of their reciprocals is 1/12
Answer by nabla(475) About Me  (Show Source):
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a
a+1
1%2Fa+-+1%2F%28a%2B1%29=1%2F12
%28a%2B1-a%29%2F%28a%28a%2B1%29%29=1%2F12
1%2F%28a%28a%2B1%29%29=1%2F12
This implies
%28a%28a%2B1%29%29=12
a%5E2%2Ba-12=0
%28a%2B4%29%28a-3%29=0
Gives a=-4 or a=3, a must be positive so we exclude -4 from the answer set.
So the numbers are 3, 3+1=4
Now, check:
1/3 -1/4=4/12 -3/12=1/12.