The text extraction from the image didn't yield any results. However, I can solve the expression visually.

The given mathematical expression is: $\left(\frac{-9}{12}\right) + \frac{5}{8} \times \frac{4}{5} \div \frac{4}{12} + \frac{3}{4}$

Step 1: Simplify the fractions

1. Simplify $\frac{-9}{12}$: $\frac{-9}{12} = \frac{-3}{4}$

2. $\frac{5}{8} \times \frac{4}{5}$ simplifies to: $\frac{5 \times 4}{8 \times 5} = \frac{4}{8} = \frac{1}{2}$

3. Next, $\frac{1}{2} \div \frac{4}{12}$ simplifies to: $\frac{1}{2} \times \frac{12}{4} = \frac{12}{8} = \frac{3}{2}$

Step 2: Combine all terms

Now, we substitute these into the expression: $\frac{-3}{4} + \frac{3}{2} + \frac{3}{4}$

Step 3: Find the common denominator and add fractions

The common denominator for the fractions is 4:

1. $\frac{3}{2} = \frac{6}{4}$
2. Now, add them: $\frac{-3}{4} + \frac{6}{4} + \frac{3}{4} = \frac{6}{4} = \frac{3}{2}$

Final Answer:

The result of the expression is $\frac{3}{2}$.

Would you like more details or have any questions?

Here are five related questions you might find interesting:

1. How do you simplify fractions with different denominators?
2. What is the order of operations in complex expressions?
3. How can you convert improper fractions to mixed numbers?
4. How would you handle similar expressions if they involved decimals?
5. Can you solve expressions that involve both fractions and exponents?

Tip: Always check for simplification at each step, as it makes calculations more manageable!