Let's simplify the expression \( \frac{4x^2 - 12x + 24}{4x} \).

### Step-by-Step Solution:

1. **Distribute the denominator across the numerator**:
   \[
   \frac{4x^2}{4x} - \frac{12x}{4x} + \frac{24}{4x}
   \]

2. **Simplify each term individually**:
   - The first term: 
     \[
     \frac{4x^2}{4x} = \frac{4 \cdot x^2}{4 \cdot x} = x
     \]
   - The second term: 
     \[
     \frac{12x}{4x} = \frac{12 \cdot x}{4 \cdot x} = 3
     \]
   - The third term: 
     \[
     \frac{24}{4x} = \frac{24}{4} \cdot \frac{1}{x} = 6 \cdot \frac{1}{x} = \frac{6}{x}
     \]

3. **Combine the simplified terms**:
   \[
   x - 3 + \frac{6}{x}
   \]

So, the simplified expression is:

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

Would you like further details on any part of this solution?

### Related Questions:
1. How would the solution change if the expression was \( 4x^2 - 12x + 24x \)?
2. What happens if you divide each term in \( 4x^2 - 12x + 24 \) separately by \( x \) instead of \( 4x \)?
3. How can you factor the expression \( 4x^2 - 12x + 24 \) before dividing by \( 4x \)?
4. What if the expression was \( 4x^3 - 12x^2 + 24x \)? How would you simplify it?
5. How would you graph the expression \( x - 3 + \frac{6}{x} \)?

**Tip:** When simplifying rational expressions, always check if the numerator can be factored to simplify the expression further before dividing.

Simplify the rational expression 4x^2 - 12x + 24 / 4x with a detailed step-by-step solution. Learn how to distribute division across terms and simplify algebraic fractions. This solution is ideal for students in Grades 9-10 exploring key concepts in algebra.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation