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 29. find the two positive integers.

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