It seems like you're asking to simplify the expression:

$\frac{9x^2 - 3x + 12}{3x}$

Let's simplify it step by step:

Step 1: Break it into separate terms

We can divide each term in the numerator by the denominator $3x$.

$\frac{9x^2}{3x} - \frac{3x}{3x} + \frac{12}{3x}$

Step 2: Simplify each term

• $\frac{9x^2}{3x} = 3x$ (since $9x^2 \div 3x = 3x$)
• $\frac{3x}{3x} = 1$
• $\frac{12}{3x} = \frac{4}{x}$

Step 3: Combine the terms

Now we can put it all together:

$3x - 1 + \frac{4}{x}$

Thus, the simplified expression is:

$3x - 1 + \frac{4}{x}$

Would you like any further details or a deeper explanation of these steps?

Here are 5 related questions you might find interesting:

1. How do you factor quadratic expressions like $9x^2 - 3x + 12$?
2. What happens if you try to simplify a rational expression with different powers of $x$?
3. How do you handle negative exponents when simplifying rational expressions?
4. Can you apply the same process to higher-degree polynomials in rational expressions?
5. What is the concept of domain in rational expressions, and how does it affect your simplifications?

Tip: Always try to break complex expressions into smaller, more manageable parts. It can make simplifying easier and less prone to mistakes.