Which of the following is the simplified form of 18x^2-12x+6/3x

A.6x-2
B.6x^2-4x+2
C.6x^3-4x^2+2x
D.6x-4+2/x

1 answer

To simplify the expression \(\frac{18x^2 - 12x + 6}{3x}\), we can start by factoring out the common factor from the numerator.

First, we notice that each term in the numerator, \(18x^2\), \(-12x\), and \(6\) has a common factor of \(6\):

\[ 18x^2 - 12x + 6 = 6(3x^2 - 2x + 1) \]

Now, we can rewrite the entire expression:

\[ \frac{18x^2 - 12x + 6}{3x} = \frac{6(3x^2 - 2x + 1)}{3x} \]

Next, we simplify the fraction:

\[ = \frac{6}{3x}(3x^2 - 2x + 1) \]

The \(6\) and \(3\) simplify:

\[ = \frac{6}{3} \cdot \frac{(3x^2 - 2x + 1)}{x} = 2 \cdot \frac{(3x^2 - 2x + 1)}{x} = 2(3x - 2 + \frac{1}{x}) = 6x - 4 + \frac{2}{x} \]

Now we can organize our simplified terms:

This leads us to:

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

So the simplified form of the expression is:

Option D: \(6x - 4 + \frac{2}{x}\).