5) \( \frac{\frac{4}{3}-\frac{1}{7}}{2+\frac{\frac{1}{2}}{6}} \)

To solve the expression \( \frac{\frac{4}{3}-\frac{1}{7}}{2+\frac{\frac{1}{2}}{6}} \), let’s break it down step by step. First, simplify the numerator: 1. Find a common denominator between \( \frac{4}{3} \) and \( \frac{1}{7} \), which is 21. 2. Rewrite \( \frac{4}{3} \) as \( \frac{28}{21} \) and \( \frac{1}{7} \) as \( \frac{3}{21} \). 3. Now, compute \( \frac{28}{21} - \frac{3}{21} = \frac{25}{21} \). Next, simplify the denominator: 1. For \( 2 + \frac{\frac{1}{2}}{6} \), first simplify \( \frac{\frac{1}{2}}{6} \). 2. This becomes \( \frac{1}{2} \times \frac{1}{6} = \frac{1}{12} \). 3. Thus, the denominator is \( 2 + \frac{1}{12} \). 4. Convert 2 to have a common denominator of 12, \( 2 = \frac{24}{12} \), so \( \frac{24}{12} + \frac{1}{12} = \frac{25}{12} \). Now the expression can be rewritten as: \[ \frac{\frac{25}{21}}{\frac{25}{12}} = \frac{25}{21} \times \frac{12}{25} \] The \( 25 \) cancels out: \[ = \frac{12}{21} \] Finally, simplify \( \frac{12}{21} \) to \( \frac{4}{7} \). Thus, the final answer is: \[ \frac{4}{7} \]