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Let's break down and simplify the given expression step by step.

The expression is:

\[
\frac{3^2 + 4 \times 3}{|-3 + (-4)|}
\]

### Step 1: Simplify the numerator
The numerator is \(3^2 + 4 \times 3\).

- \(3^2 = 9\)
- \(4 \times 3 = 12\)

So, the numerator becomes:
\[
9 + 12 = 21
\]

### Step 2: Simplify the denominator
The denominator is the absolute value of \(-3 + (-4)\).

- \(-3 + (-4) = -3 - 4 = -7\)
- The absolute value of \(-7\) is \(7\), because \(|-7| = 7\).

### Step 3: Final expression
Now, the simplified expression is:
\[
\frac{21}{7} = 3
\]

Thus, the simplified value of the expression is **3**.

Would you like a more detailed explanation of any step?

Here are five related questions for further practice:
1. What is the result of \(\frac{4^2 + 2 \times 5}{|-5 + (-6)|}\)?
2. Simplify \(\frac{5^2 + 3 \times 4}{|-2 + (-7)|}\).
3. How do absolute values affect expressions with negative numbers?
4. What is the simplified form of \(\frac{2^3 + 5 \times 1}{|-4 + (-5)|}\)?
5. Can you evaluate \(\frac{6^2 + 4 \times 2}{|3 - 8|}\)?

**Tip:** Always evaluate the absolute value after simplifying the expression inside it.

Simplify the expression \(\frac{3^2 + 4 \times 3}{|-3 + (-4)|}\).

Learn how to simplify the expression \(\frac{3^2 + 4 \times 3}{|-3 + (-4)|}\) with a step-by-step breakdown. This exercise includes key mathematical concepts such as order of operations and absolute values. Suitable for students in Grades 6-8.

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