1. **State the problem:** We are given the equation $$V = \frac{1}{U} + \frac{1}{W}$$ and asked to solve for $U$. 2. **Isolate the term with $U$:** Start by subtracting $$\frac{1}{W}$$ from both sides: $$V - \frac{1}{W} = \frac{1}{U}$$ 3. **Rewrite the equation:** We now have $$\frac{1}{U} = V - \frac{1}{W}$$ 4. **Find a common denominator on the right side:** $$V - \frac{1}{W} = \frac{VW}{W} - \frac{1}{W} = \frac{VW - 1}{W}$$ 5. **Rewrite the equation:** $$\frac{1}{U} = \frac{VW - 1}{W}$$ 6. **Take the reciprocal of both sides to solve for $U$:** $$U = \frac{W}{VW - 1}$$ **Final answer:** $$U = \frac{W}{VW - 1}$$