The sum of the reciprocals of two even consecutive even numbers is 7\24. Find the numbers. I did 1 over x + 1 over x = 7\24, but that didn't work. What did I do wrong?

Question

The sum of the reciprocals of two even consecutive even numbers is 7\24.  Find the numbers. I did 1 over x + 1 over x = 7\24, but that didn't work. What did I do wrong?

mathstudent55 · Answer

Even numbers are x and x + 2, not x and x + 1

campbell_st · Answer

well let the consecutive numbers be x and x + 2

the reciprocals are 

1/x and 1/(x+2)

so you now have an equation 

$$\frac{1}{x} + \frac{1}{x +2} = \frac{7}{24}$$

mathstudent55 · Answer

Luis, the problem states " two even consecutive even numbers "
You are making the same mistake the OP made.

anonymous · Answer

do I have to make the denominators of each number the same?

anonymous · Answer

or would I multiply the first number by x and the other number by x + 2 and then multiply 7\24 by x + x + 2?

mathstudent55 · Answer

"doent matter, ;se expresa de la misma forma !!"
x and x + 2 is not the same as x and x + 1

mathstudent55 · Answer

Get the LCD of the 3 denominators and multiply all fractions by the LCD. This will eliminate all denominators from the equation.

mathstudent55 · Answer

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