To simplify the expression [tex]\(\frac{18 x^2 - 12 x + 6}{3 x}\)[/tex], follow these steps:
1. Separate the Terms:
Split the numerator into separate terms over the common denominator [tex]\(3x\)[/tex]:
[tex]\[
\frac{18 x^2}{3 x} - \frac{12 x}{3 x} + \frac{6}{3 x}
\][/tex]
2. Simplify Each Term Individually:
- For the first term:
[tex]\[
\frac{18 x^2}{3 x} = \frac{18}{3} \cdot \frac{x^2}{x} = 6 x
\][/tex]
- For the second term:
[tex]\[
\frac{12 x}{3 x} = \frac{12}{3} \cdot \frac{x}{x} = 4
\][/tex]
- For the third term:
[tex]\[
\frac{6}{3 x} = \frac{6}{3} \cdot \frac{1}{x} = 2 \cdot \frac{1}{x} = \frac{2}{x}
\][/tex]
3. Combine the Simplified Terms:
Bring together all the simplified terms:
[tex]\[
6 x - 4 + \frac{2}{x}
\][/tex]
Thus, the simplified form of the expression [tex]\(\frac{18 x^2 - 12 x + 6}{3 x}\)[/tex] is:
[tex]\[
6 x - 4 + \frac{2}{x}
\][/tex]
So, the correct answer is:
[tex]\[
\boxed{6 x - 4 + \frac{2}{x}}
\][/tex]
