1. **State the problem:** Solve the equation $$\frac{1}{a} + \frac{1}{b} = 2$$ for one variable in terms of the other. 2. **Formula and rules:** To combine fractions, find a common denominator. Here, the common denominator is $ab$. 3. **Combine the fractions:** $$\frac{1}{a} + \frac{1}{b} = \frac{b}{ab} + \frac{a}{ab} = \frac{a+b}{ab}$$ 4. **Set equal to 2:** $$\frac{a+b}{ab} = 2$$ 5. **Multiply both sides by $ab$ to clear the denominator:** $$\cancel{ab} \cdot \frac{a+b}{\cancel{ab}} = 2 \cdot ab$$ $$a+b = 2ab$$ 6. **Solve for $a$ in terms of $b$:** $$a + b = 2ab$$ $$a - 2ab = -b$$ $$a(1 - 2b) = -b$$ 7. **Divide both sides by $(1 - 2b)$:** $$a = \frac{-b}{1 - 2b}$$ This is the expression for $a$ in terms of $b$. **Final answer:** $$a = \frac{-b}{1 - 2b}$$