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As $\frac{1}{x} = 3.5 = \frac{7}{2}$, so $x = \frac{2}{7}$.
Then $x+2 = \frac{16}{7}$.
Hence $\frac{1}{x+2} = \frac{7}{16}$.
This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.