$\frac{x+\frac{1}{2}}{2+\frac{1}{x}}=$

Step 1 ：Given the complex fraction \(\frac{x+\frac{1}{2}}{2+\frac{1}{x}}\)

Step 2 ：To simplify it, we can multiply the numerator and the denominator by \(2x\) to get rid of the fractions within the fractions.

Step 3 ：This results in the expression \(x^2\).

Step 4 ：However, this is not the final answer. We need to divide \(x^2\) by \(2x\) to get the final simplified form of the original expression.

Step 5 ：The final simplified form of the original expression is \(0.5x\).

Step 6 ：Final Answer: \(\boxed{0.5x}\)