Apositive integer is twice another. the sum of the reciprocals of the two positive integers is 3/10. find the two integers.

Let's call the integers and . The first information (one is twice the other) translates as .

The second information about the sum of reciprocals can be written as

But since we know that , we can rewrite this expression as

Since the numerators of both fractions equal 3, then the denominators must be equal as well. So, we have

And since we know that .