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The problem asks to simplify the expression:

\[
\frac{4x^2 - 12x + 24}{4x}
\]

### Steps for simplification:

1. **Divide each term in the numerator by the denominator (4x):**

   \[
   \frac{4x^2}{4x} - \frac{12x}{4x} + \frac{24}{4x}
   \]

2. Simplify each term:

   - \(\frac{4x^2}{4x} = x\)
   - \(\frac{12x}{4x} = 3\)
   - \(\frac{24}{4x} = \frac{6}{x}\)

So, the simplified expression is:

\[
x - 3 + \frac{6}{x}
\]

This is the expression in standard form.

Would you like further details or have any questions? Here are 5 related questions to consider:

1. What is polynomial long division and how does it differ from regular division?
2. Can this expression be simplified further using factoring techniques?
3. How do you handle expressions where the denominator is not a monomial?
4. How does the domain of the simplified expression change after dividing by \(x\)?
5. What happens to the expression when \(x = 0\)?

**Tip:** Always check for restrictions on the variable after simplification, especially if division by a variable occurs!

Simplify (4x^2 - 12x + 24) / 4x. Write your answer in standard form.

This problem guides students through simplifying the polynomial expression (4x^2 - 12x + 24) / 4x. Learn how to divide each term in the polynomial by 4x, breaking down the process step-by-step. Suitable for Grades 8-10.

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