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Answer in an easy and simple way for kids

Let's break this down in a simple way:

We are asked to simplify the expression:

\[
\frac{18x^4 - 3x^2 + 6x - 4}{6x}
\]

### Step-by-step solution:

1. **Split each term in the numerator by \(6x\):**
   We are going to divide each term on top by \(6x\):

   \[
   \frac{18x^4}{6x} - \frac{3x^2}{6x} + \frac{6x}{6x} - \frac{4}{6x}
   \]

2. **Simplify each term:**
   - For the first term: \(\frac{18x^4}{6x} = 3x^3\)
   - For the second term: \(\frac{3x^2}{6x} = \frac{1}{2}x\)
   - For the third term: \(\frac{6x}{6x} = 1\) (since anything divided by itself is 1)
   - For the last term: \(\frac{-4}{6x} = \frac{-2}{3x}\) (simplifying the fraction \( \frac{-4}{6} = -\frac{2}{3}\))

3. **Final simplified expression:**
   Now we put everything together:

   \[
   3x^3 - \frac{1}{2}x + 1 - \frac{2}{3x}
   \]

So, the simplified expression is:

\[
3x^3 - \frac{1}{2}x + 1 - \frac{2}{3x}
\]

Would you like to go over any of the steps in more detail or have any questions?

Here are 5 questions that are related to this topic:
1. How do we simplify an expression with a variable in the denominator?
2. What is the process to simplify each term in a polynomial division?
3. Why do we need to split each term in the numerator by the denominator?
4. What happens if a term in the numerator does not contain the variable in the denominator?
5. How can we handle negative exponents during simplification?

**Tip:** Always remember to divide each term individually when simplifying complex fractions!

Simplify the expression: (18x^4 - 3x^2 + 6x - 4) / 6x

Learn how to simplify the polynomial expression (18x^4 - 3x^2 + 6x - 4) / 6x through step-by-step division of each term in the numerator by the denominator. This problem covers key algebraic concepts like polynomial division and fraction simplification, suitable for students in Grades 8-10.

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