SOLUTION: Consider two consecutive even integers such that twice the reciprocal of the smaller integer added to the reciprocal of the larger integer is equal to two-thirds. What are the inte

Question 1019842: Consider two consecutive even integers such that twice the reciprocal of the smaller integer added to the reciprocal of the larger integer is equal to two-thirds. What are the integers?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
x and x+2 are the numbers
(2/x)+(1/x+2)=2/3
clear fractions by multiplying by 3(x)(x+2)
6x+12+3x=2x^2+4x
9x+12=2x^2+4x
0=2x^2-5x-12
(2x+3)(x-4)=0
only integer root is x=4 (the other is -3/2)
x+2=6
numbers are 4,6
2(1/4)+(1/6)=(1/2)+(1/6)=(2/3)

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