SOLUTION: The difference of the reciprocals of two consecutive even integers is 1/24. Find the integers. Thanks -tom

Question 49954: The difference of the reciprocals of two consecutive even integers is 1/24. Find the integers. Thanks
-tom
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Let the two consecutive integers be a and a+2.
You can write:
Simplify the left side.
Now cross-multiply.
Subtract 48 from both sides of the equation.
Factor this.
Apply the zero product principle.
and/or
If then
If then
Since you did not restrict the integers to positive integers only, there are two answers:
6 and 8
-8 and -6
Check the positive integers first:
Simplify.

This checks!
Now the negative integers:
Simplify.

This also checks!
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