Simplify the complex fraction as much as possible. Leave your answer as a proper fraction or a mixed number 3+2/3 / 3 - 2/3 = 

To simplify the complex fraction \(\frac{3 + \frac{2}{3}}{3 - \frac{2}{3}}\), let's first convert the mixed numbers into improper fractions:

### Step 1: Express as Improper Fractions

The expression can be rewritten by representing the whole numbers as fractions with a common denominator:

\[
3 = \frac{9}{3}
\]

So:

\[
3 + \frac{2}{3} = \frac{9}{3} + \frac{2}{3} = \frac{11}{3}
\]

Similarly:

\[
3 - \frac{2}{3} = \frac{9}{3} - \frac{2}{3} = \frac{7}{3}
\]

Now the complex fraction is:

\[
\frac{\frac{11}{3}}{\frac{7}{3}}
\]

### Step 2: Simplify the Complex Fraction

To divide by a fraction, multiply by its reciprocal:

\[
\frac{11}{3} \div \frac{7}{3} = \frac{11}{3} \times \frac{3}{7}
\]

The 3's cancel out:

\[
= \frac{11}{7}
\]

### Step 3: Check if the Fraction is Proper

\(\frac{11}{7}\) is an improper fraction. To express it as a mixed number:

\[
\frac{11}{7} = 1 \frac{4}{7}
\]

### Final Answer

The simplified expression is:

\[
\frac{11}{7} \text{ or } 1 \frac{4}{7}.
\]

Would you like further details on any step, or do you have any questions?

### Related Questions

1. How do you add and subtract fractions with different denominators?
2. How do you convert improper fractions to mixed numbers?
3. What is the reciprocal of a fraction and how is it used in division?
4. How do you simplify complex fractions in general?
5. What are some other examples of simplifying complex fractions?

**Tip:** Always remember to convert whole numbers to fractions with a common denominator when simplifying expressions involving fractions!

Simplify the complex fraction as much as possible. Leave your answer as a proper fraction or a mixed number 3+2/3 / 3 - 2/3 =

Learn how to simplify the complex fraction (3 + 2/3) / (3 - 2/3) into a proper or mixed number. This problem involves key concepts like improper fractions, division of fractions, and simplifying mixed numbers. Detailed solution for students in Grades 6-8.

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