how to write this in an algebraic expression

Question

A positive integer is twice another. The sum of the reciprocals of the two positive integers is. Find the two integers.

Answer 1

x=2y

x,y>0

1/x + 1/y =?

1/2y + 1/y

= (1/2y)(1+2)

= 3/2y

x=2, y=1

x=4 y=2

x=-2, y=-1

x=-4, y=-2

an infinite number of possible solutions

1/2 + 1/1 = 3/2

1/4 + 1/2= 3/4= 3/2(2)

and endless other x y values

unless you intended to finish the restriction as to the sum of reciprocals to a specific number

such as

1/x +1/y = 8

then

1/2y + 1/y = 8

1 + 2= 8(2y) = 16y

y = 3/16

x = 3/8

8/3 + 16/3 = 24/3 = 8