1. The problem is to simplify the expression $$\left(\frac{1}{2} + \frac{1}{x}\right)$$. 2. The formula to add fractions is $$\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}$$. 3. Applying this to our expression, we find a common denominator which is $$2x$$. 4. Rewrite each fraction with the common denominator: $$\frac{1}{2} = \frac{x}{2x}$$ $$\frac{1}{x} = \frac{2}{2x}$$ 5. Add the numerators: $$\frac{x}{2x} + \frac{2}{2x} = \frac{x + 2}{2x}$$ 6. So, the simplified form of $$\left(\frac{1}{2} + \frac{1}{x}\right)$$ is: $$\boxed{\frac{x + 2}{2x}}$$