$$ \frac{\left(4\cdot2+5-10\right)}{3+\frac{7}{3.5-2+\frac{11}{5.5}}} $$

To solve the given expression, we need to simplify both the numerator and the denominator step-by-step. The expression is:

\[
\frac{\left(4 \cdot 2 + 5 - 10\right)}{3 + \frac{7}{3.5 - 2 + \frac{11}{5.5}}}
\]

### Step 1: Simplify the Numerator

The numerator is:

\[
4 \cdot 2 + 5 - 10
\]

Calculating step-by-step:

\[
4 \cdot 2 = 8
\]

\[
8 + 5 = 13
\]

\[
13 - 10 = 3
\]

So, the numerator is $3$.

### Step 2: Simplify the Denominator

The denominator is:

\[
3 + \frac{7}{3.5 - 2 + \frac{11}{5.5}}
\]

#### Step 2.1: Simplify the Innermost Fraction

\[
\frac{11}{5.5} = 2
\]

#### Step 2.2: Continue Simplifying Inside the Denominator

Now, substitute the simplified fraction back into the expression:

\[
3.5 - 2 + 2
\]

Calculate:

\[
3.5 - 2 = 1.5
\]

\[
1.5 + 2 = 3.5
\]

#### Step 2.3: Simplify the Main Fraction in the Denominator

Now, substitute back into the main fraction:

\[
\frac{7}{3.5} = 2
\]

#### Step 2.4: Complete the Denominator

Now we add this result to the remaining part:

\[
3 + 2 = 5
\]

So, the denominator is $5$.

### Step 3: Form the Final Expression

Now, we have:

\[
\frac{3}{5}
\]

### Conclusion

The simplified result of the expression is:

\[
\frac{3}{5}
\]

Would you like more details or have any questions?

Here are 5 related questions to explore further:

1. How would you simplify a more complex fraction with nested terms?
2. What is the result of $\frac{6}{4 + \frac{3}{2}}$?
3. How do you handle expressions with multiple operations, like $(5 + 2 \times 3) - 4$?
4. How do you convert a fraction like $\frac{3}{5}$ to a decimal?
5. What happens when you multiply two fractions, such as $\frac{3}{5} \times \frac{2}{7}$?

**Tip:** When dealing with fractions in complex expressions, always simplify the innermost fractions first!

Learn how to simplify the complex fraction expression (4*2 + 5 - 10) / (3 + 7 / (3.5 - 2 + 11 / 5.5)) step-by-step. Understand the order of operations and how to handle nested fractions effectively. Suitable for high school students.

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