SOLUTION: I need help solving this problem: The sum of the reciprocals of two consecutive integers is 5/6 (this should look like a fraction 5 over 6). Find the integers. Thank you i

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Question 280750: I need help solving this problem:
The sum of the reciprocals of two consecutive integers is 5/6 (this should look like a fraction 5 over 6).
Find the integers.
Thank you in advance. It says in the directions if there is no solution to write "no solution".

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
I need help solving this problem:
The sum of the reciprocals of two consecutive integers is 5/6 (this should look like a fraction 5 over 6).
Find the integers.
Thank you in advance. It says in the directions if there is no solution to write "no solution". 

Let the consecutive integers be n and n+1:                                                                                                      
1%2Fn+%2B+1%2F%28n%2B1%29=5%2F6

The LCD is 6n%28n%2B1%29

Multiply through by this LCD





6%28n%2B1%29+%2B+6n=5n%28n%2B1%29

6n%2B6%2B6n+=+5n%5E2%2B5n

12n%2B6=5n%5E2%2B5n

0=5n%5E2-7n-6

0=%285n%2B3%29%28n-2%29

5m%2B3=0 gives solution n=-3%2F5

n-2=0 gives solution n=2

We discard the fractional solution, since it is not an integer.

So the only solution is 2,

so the consecutive integers are 2 and 3:

Checking:

1%2F2%2B1%2F3=3%2F6%2B2%2F6=5%2F6

It checks.

Edwin