the correct question is
One positive integer is 3 units more than another. When the reciprocal of the larger is subtracted from twice the reciprocal of the smaller, the result is 2/9. Find the two positive integers.
let
x-------> the positive larger integer
y------> the positive smaller integer
we know that
x=3+y------> equation 1
2*(1/y)-(1/x)=29-----> equation 2
substitute equation 1 in equation 2
2*(1/y)-(1/(y+3))=2/9
[2*(y+3)-y]/[y*(y+3)]=2/9
9*[2y+6-y]=2*[y²+3y]
9*[y+6]=2y²+6y
9y+54=2y²+6y
2y²-3y-54=0
using a graphical tool to resolve the second order equation
see the attached figure
the solution is
y=6
so
x=y+3------> x=6+3-----> x=9
the answer is
the numbers are
9 and 6
