1. **State the problem:** Rearrange the equation $$\frac{p}{q r} = 3 + \frac{1}{q}$$ to make $r$ the subject. 2. **Start with the given equation:** $$\frac{p}{q r} = 3 + \frac{1}{q}$$ 3. **Combine the right side into a single fraction:** Since $3 = \frac{3q}{q}$, we have $$3 + \frac{1}{q} = \frac{3q}{q} + \frac{1}{q} = \frac{3q + 1}{q}$$ 4. **Rewrite the equation:** $$\frac{p}{q r} = \frac{3q + 1}{q}$$ 5. **Cross-multiply to eliminate denominators:** $$p \cdot q = q r \cdot (3q + 1)$$ 6. **Simplify left side:** $$p q = q r (3q + 1)$$ 7. **Divide both sides by $q (3q + 1)$ to isolate $r$:** $$r = \frac{p q}{q (3q + 1)}$$ 8. **Cancel $q$ in numerator and denominator:** $$r = \frac{p}{3q + 1}$$ **Final answer:** $$r = \frac{p}{3q + 1}$$