SOLUTION: The sum of the reciprocals of two consecutive even number is 7/24. Find the number...I can't figure out how to do this problem

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Question 125400: The sum of the reciprocals of two consecutive even number is 7/24. Find the number...I can't figure out how to do this problem
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
n is the 1st number
n+%2B+2 is the 2nd number
%281+%2F+n%29+%2B+%281+%2F+%28n+%2B+2%29%29+=+7%2F24
multiply both sides by n%2A%28n%2B2%29
%28n+%2B+2%29+%2B+n+=+%287%2F24%29%2An%2A%28n+%2B+2%29
multiply both sides by 24
24%2A%282n+%2B+2%29+=+7n%5E2+%2B+14n
48n+%2B+48+=+7n%5E2+%2B+14n
7n%5E2+-+34n+-+48+=+0
%287n+%2B+8%29%28n+-+6%29+=+0
n+=+-%288%2F7%29
I reject this since it's not a whole number and negative
and
n+=+6
n+%2B+2+=+8
The numbers are 6 and 8
check:
%281%2F6%29+%2B+%281%2F8%29+=+7%2F24
multiply both sides by 48
8+%2B+6+=+14
14+=+14
OK