SOLUTION: Find two consecutive even integers such that the sum of the first and the reciprocal of the second is 9/4. This problem we are to come up with the formula and write it out as i

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Question 294980: Find two consecutive even integers such that the sum of the first and the reciprocal of the second is 9/4.

This problem we are to come up with the formula and write it out as if we were teaching someone how to do it.
So far I think it should look like this (but not really sure):
1/x+1/x+1=9/4. If I am going in the right direction, I can complete the problem. Im just not sure this is how to set it up.
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
1/x+1/x+1=9/4
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Let x & (x+2) be the 2 consecutive EVEN integers.
The reciprocal of the second integer is 1/(x+2)
x+1/(x+2)=9/4
Find the common denominator for the left side terms.
[x(x+2)+1]/(x+2)=9/4
[x^2+2x+1)/(x+2)=9/4
Cross multiply.
4(x^2+2x+1)=9(x+2)
4x^2+8x+4=9x+18
4x^2+8x-9x+4-18=0
4x^2-x-14=0
(4x+7)(x-2)=0
x-2=0
x=2 ans. for the first even integer.
2+2=4 ans. for the second even integer.
Proof:
2+1/(2+2)=9/4
2+1/4=9/4
8/4+1/4=9/4
9/4=9/4