As $\frac{1}{x} = 3.5 = \frac{7}{2}$, so $x = \frac{2}{7}$.

Then $x+2 = \frac{16}{7}$.

Hence $\frac{1}{x+2} = \frac{7}{16}$.

Then $x+2 = \frac{16}{7}$.

Hence $\frac{1}{x+2} = \frac{7}{16}$.

*This problem is taken from the UKMT Mathematical Challenges.*