SOLUTION: The sum of the reciprocals of two consecutive even integers is 7/24. Find these integers.

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Question 151172: The sum of the reciprocals of two consecutive even integers is 7/24. Find these integers.
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
1/X+1/(X+2)=7/24
(X+2+X)/X(X+2)=7/24
(2X+2)/X^2+2X=7/24
7(X^2+2X)=24(2X+2)
7X^2+14X=48X+48
7X^2+14X-48X-48=0
7X^2-34X-48=0
(7X+8)(X-6)=0
X-6=0
X=6 ANSWER FOR THE SMALLER INTEGER.
6+2=8 FOR THE LARGER INTEGER.
PROOF:
1/6+1/8=7/24
(8+6)/48=7/24
14/48=7/24
7/24=7/24