SOLUTION: The difference between the reciprocal of two consecutive positive even number is 1/12. Find the two numbers.

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Question 191912: The difference between the reciprocal of two consecutive positive even number is 1/12. Find the two numbers.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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The difference between the reciprocal of two consecutive positive even number is 1/12. Find the two numbers.:
:
Two numbers x, (x+2)
:
The equation for the above statement:
1%2F%28x%2B2%29 - 1%2Fx = 1%2F12
;
Multiply equation by 12x(x+2)
12x(x+2)*1%2F%28x%2B2%29 - 12x(x+2)*1%2Fx = 12x(x+2)*1%2F12
Cancel out the denominators and you have:
12x - 12(x+2) = x(x+2)
:
12x - 12x + 24 = x^2 + 2x
:
0 = x^2 + 2x - 24; a quadratic equation
Factors to:
(x+6)(x-4) = 0
positive solution
x = 4, and 6 are the two numbers
;
:
Check solution in our original equation
1%2F4 - 1%2F6 = 1%2F12
3%2F12 - 2%2F12 = 1%2F12