SOLUTION: please help me answer the following problem: find two consecutive positive even integers the difference of whose reciprocals is 1/60. thanks javier

Question 24844: please help me answer the following problem:
find two consecutive positive even integers the difference of whose reciprocals is 1/60.
thanks
javier
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Try this Javier: Let n be the first positive even integer and n+2 be the next consecutive positive even integer. You can write the problem as:
Add the fractions on the left. The common denominator is
Simplify and solve for n.
Multiply both sides of the equation by 60.
Multiply both sides by
Subtract 120 from both sides.
Solve for n by factoring.
Apply the zero products principle.
and/or
If then This is the first positive even integer.
If the Discard this solution as it is a negative integer.
The two integere are:
n = 10 and n+2 = 12
10 and 12
Check:
=

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