A positive integers is twice another. The difference of the reciprocals of the two positive integers is (1/18). Find the two integers.

Let the integers be \( x \) and \( y \), where \( y = 2x \).

The reciprocals of the integers are \( \frac{1}{x} \) and \( \frac{1}{y} \), respectively.

The difference of the reciprocals is given by:
\frac{1}{x} - \frac{1}{y} = \frac{1}{18}

Substitute \( y = 2x \) into the equation:
\frac{1}{x} - \frac{1}{2x} = \frac{1}{18}

Simplify the left side:
\frac{2 - 1}{2x} = \frac{1}{18}

This reduces to:
\frac{1}{2x} = \frac{1}{18}

Solve for \( x \):
2x = 18
x = 9

If \( x = 9 \):
y = 2x = 18

So the two integers are:
x = 9, \quad y = 18