We can evaluate the given expression by first simplifying the expressions inside the parentheses and then performing the division. Here are the steps to simplify the expression:

1. Start with the given expression: \(\frac{\left(\frac{3}{8}\div\frac{1}{2}+\frac{1}{2}\right)}{\left(\frac{1}{8}\times\frac{2}{3}+\frac{1}{3}\right)}\)

2. Simplify the expressions inside the parentheses: \(\frac{\left(\frac{3}{8}\div\frac{1}{2}+\frac{1}{2}\right)}{\left(\frac{1}{8}\times\frac{2}{3}+\frac{1}{3}\right)} = \frac{\left(\frac{3}{4}+\frac{1}{2}\right)}{\left(\frac{1}{12}+\frac{1}{3}\right)} = \frac{\left(\frac{5}{4}\right)}{\left(\frac{5}{12}\right)}\)

3. Use the property that dividing by a fraction is equivalent to multiplying by its reciprocal: \(\frac{\left(\frac{5}{4}\right)}{\left(\frac{5}{12}\right)} = \left(\frac{5}{4}\right) \times \left(\frac{12}{5}\right) = 3\)

So, after simplifying the given expression, we get 3,