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!