1. **State the problem:** Rearrange the equation $$a = b \left( \frac{1}{c} - \frac{1}{d} \right)$$ to isolate $c$. 2. **Start by dividing both sides by $b$ to isolate the parentheses:** $$\frac{a}{b} = \frac{1}{c} - \frac{1}{d}$$ 3. **Add $\frac{1}{d}$ to both sides to isolate $\frac{1}{c}$:** $$\frac{a}{b} + \frac{1}{d} = \frac{1}{c}$$ 4. **Combine the left side into a single fraction:** $$\frac{a}{b} + \frac{1}{d} = \frac{ad}{bd} + \frac{b}{bd} = \frac{ad + b}{bd}$$ 5. **So we have:** $$\frac{1}{c} = \frac{ad + b}{bd}$$ 6. **Take the reciprocal of both sides to solve for $c$:** $$c = \frac{bd}{ad + b}$$ **Final answer:** $$c = \frac{bd}{ad + b}$$