https://file.aiquickdraw.com/mathbot/file/17268940015744p1t34br.jpg

The image shows a mathematical expression involving fractions in both the numerator and the denominator. The expression is:

\[
\frac{\left( \frac{3}{1} + \frac{1}{2} \right) + \left( \frac{2}{1} + \frac{3}{4} \right)}{\left( \frac{1}{2} + \frac{1}{3} \right) + 2}
\]

Let's break this down step by step:

### Numerator:
1. \( \frac{3}{1} + \frac{1}{2} \)
   - Common denominator: 2.
   - \( 3 = \frac{6}{2} \), so \( \frac{6}{2} + \frac{1}{2} = \frac{7}{2} \).

2. \( \frac{2}{1} + \frac{3}{4} \)
   - Common denominator: 4.
   - \( 2 = \frac{8}{4} \), so \( \frac{8}{4} + \frac{3}{4} = \frac{11}{4} \).

Therefore, the entire numerator is:
\[
\frac{7}{2} + \frac{11}{4}
\]
   - Common denominator: 4.
   - \( \frac{7}{2} = \frac{14}{4} \), so \( \frac{14}{4} + \frac{11}{4} = \frac{25}{4} \).

### Denominator:
1. \( \frac{1}{2} + \frac{1}{3} \)
   - Common denominator: 6.
   - \( \frac{1}{2} = \frac{3}{6} \) and \( \frac{1}{3} = \frac{2}{6} \), so \( \frac{3}{6} + \frac{2}{6} = \frac{5}{6} \).

2. Adding 2:
   \[
   \frac{5}{6} + 2
   \]
   - Convert 2 to \( \frac{12}{6} \), so \( \frac{5}{6} + \frac{12}{6} = \frac{17}{6} \).

### Final Expression:
Now the entire expression becomes:
\[
\frac{\frac{25}{4}}{\frac{17}{6}} = \frac{25}{4} \times \frac{6}{17} = \frac{25 \times 6}{4 \times 17} = \frac{150}{68} = \frac{75}{34}
\]

The simplified result is:
\[
\frac{75}{34}
\]

Would you like more details or have any questions?

Here are 5 related questions for practice:
1. How would you approach solving an expression with more fractions in both the numerator and denominator?
2. Can you explain how to find a common denominator for adding fractions?
3. What is the process of simplifying a complex fraction?
4. How does multiplying by the reciprocal simplify division of fractions?
5. How do you convert improper fractions to mixed numbers?

**Tip:** Always simplify complex fractions step by step to avoid confusion, especially when working with different denominators.

( (3/1 + 1/2) + (2/1 + 3/4) ) / ( (1/2 + 1/3) + 2 )

Solve a complex fraction problem involving mixed numerators and denominators. This step-by-step guide covers key mathematical concepts such as fraction addition, multiplication, and division, suitable for middle school students.

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