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The given expression is:

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

### Step-by-Step Simplification:

1. **Factor the numerator**:
   The numerator is \( 4x^2 - 12x - 24 \). First, we can factor out a common factor of \( 4 \) from the terms:
   \[
   4(x^2 - 3x - 6)
   \]

2. **Rewrite the expression**:
   Now the expression becomes:
   \[
   \frac{4(x^2 - 3x - 6)}{4x}
   \]

3. **Cancel the common factor**:
   The \( 4 \)'s in the numerator and denominator cancel out:
   \[
   \frac{x^2 - 3x - 6}{x}
   \]

4. **Simplify the remaining expression**:
   Now, divide each term in the numerator by \( x \):
   \[
   \frac{x^2}{x} - \frac{3x}{x} - \frac{6}{x} = x - 3 - \frac{6}{x}
   \]

Thus, the simplified expression in standard form is:

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

---

Do you have any questions or would you like further details?

Here are some related questions you might find helpful:
1. How do you factor polynomials with higher degrees?
2. What are the steps to simplify rational expressions?
3. Can you always cancel terms in the numerator and denominator?
4. How do you deal with division by variables in algebraic expressions?
5. What is the significance of standard form in algebraic expressions?

**Tip:** Always check for common factors in both the numerator and denominator before simplifying an expression. This can make the process easier and quicker.

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

Simplify the rational expression (4x^2 - 12x - 24) / 4x with this step-by-step solution. Learn about factoring quadratics, simplifying algebraic expressions, and standard form. Suitable for students in Grades 8-10.

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