https://file.aiquickdraw.com/mathbot/file/1725437986527pu1upu59.jpg

Let's analyze and solve the given expression step by step.

The expression provided is:

\[
E = \frac{\frac{\frac{4}{3} + \frac{2}{3} \times \frac{5}{2}}{\frac{4}{3} - 1}}{}
\]

Let's break it down:

1. **Calculate the multiplication** within the fraction:
   \[
   \frac{2}{3} \times \frac{5}{2} = \frac{10}{6} = \frac{5}{3}
   \]

2. **Add** the result to \(\frac{4}{3}\):
   \[
   \frac{4}{3} + \frac{5}{3} = \frac{9}{3} = 3
   \]

3. **Subtract** 1 from \(\frac{4}{3}\):
   \[
   \frac{4}{3} - 1 = \frac{4}{3} - \frac{3}{3} = \frac{1}{3}
   \]

4. **Divide** the sum by the difference:
   \[
   \frac{3}{\frac{1}{3}} = 3 \times 3 = 9
   \]

Therefore, the value of \( E \) is \( \boxed{9} \).

Would you like any further details or explanations on this problem? 

Here are five related questions you might find interesting:

1. How would the value of \( E \) change if the subtraction term was altered?
2. Can you express \( E \) in terms of a different variable instead of solving it numerically?
3. What if the multiplication in the numerator was replaced with division?
4. How would the problem change if all the fractions were expressed as decimals?
5. How can this expression be generalized for other fractions?

**Tip:** When working with complex fractions, it's often helpful to simplify step-by-step, focusing on basic operations first.

E = \frac{\frac{\frac{4}{3} + \frac{2}{3} \times \frac{5}{2}}{\frac{4}{3} - 1}}

This detailed solution explains how to solve a complex fraction problem involving multiplication, addition, and subtraction of fractions. Suitable for students in Grades 9-10.

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