We are asked to find the domain of the rational function $f(x) = \frac{6x+6}{3x-6}$. We need to determine which real numbers are allowed as inputs for $x$. Rational functions are defined for all real numbers except for values that make the denominator equal to zero.

1. Problem Description

We are asked to find the domain of the rational function $f(x) = \frac{6x+6}{3x-6}$. We need to determine which real numbers are allowed as inputs for $x$. Rational functions are defined for all real numbers except for values that make the denominator equal to zero.

2. Solution Steps

To find the domain of the given rational function, we need to find the values of $x$ that make the denominator equal to zero. The denominator is $3x-6$. We set the denominator equal to zero and solve for $x$:

$3x - 6 = 0$

Add 6 to both sides of the equation:

$3x = 6$

Divide both sides by 3:

$x = \frac{6}{3}$

$x = 2$

The function is undefined when $x = 2$. Therefore, the domain of $f(x)$ is all real numbers except $x = 2$.

3. Final Answer

The domain of $f(x)$ is all real numbers except

2.