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The question provided asks to perform the operation and simplify the following complex fraction:

\[
\frac{\frac{4}{3} - \frac{5}{9}}{\frac{5}{11}}
\]

### Steps to solve:

1. **Simplify the numerator:**
   We need to subtract the fractions in the numerator \(\frac{4}{3}\) and \(\frac{5}{9}\). To do this, find a common denominator. The least common denominator (LCD) of 3 and 9 is 9. Rewrite the first fraction \(\frac{4}{3}\) as \(\frac{12}{9}\):

   \[
   \frac{4}{3} = \frac{12}{9}
   \]

   Now subtract:

   \[
   \frac{12}{9} - \frac{5}{9} = \frac{12 - 5}{9} = \frac{7}{9}
   \]

2. **Now divide by the denominator:**
   The original complex fraction becomes:

   \[
   \frac{\frac{7}{9}}{\frac{5}{11}}
   \]

   To divide by a fraction, multiply by its reciprocal:

   \[
   \frac{7}{9} \times \frac{11}{5} = \frac{7 \times 11}{9 \times 5} = \frac{77}{45}
   \]

3. **Simplify the result (if needed):**
   \(\frac{77}{45}\) is already in its simplest form since 77 and 45 have no common factors.

Thus, the simplified result of the complex fraction is:

\[
\boxed{\frac{77}{45}}
\]

---

Would you like more details on any of the steps? Here are 5 related questions to explore further:

1. How do you find the least common denominator between two fractions?
2. What is the process for simplifying complex fractions in general?
3. How can you check if a fraction is in its simplest form?
4. What are the rules for multiplying and dividing fractions?
5. How would the solution change if the denominator was a mixed number?

**Tip:** Always simplify fractions as early as possible to make calculations easier!

Perform the operation and simplify the following complex fraction: (4/3 - 5/9) / (5/11).

Solve and simplify the complex fraction (4/3 - 5/9) ÷ (5/11) using fraction subtraction and multiplication techniques. This example covers the key steps of simplifying complex fractions for students in Grades 7-8.

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