Determine the Domain of the Rational Function 12/(8x-4)

To find the domain of the function $\frac{12}{8x-4}$, we must determine when the denominator equals zero and exclude these values.

Step 1: Set the denominator equal to zero and solve for $x$:

$8x - 4 = 0$

Step 2: Solve the equation $8x - 4 = 0$ for $x$:

Add 4 to both sides: $8x = 4$

Divide both sides by 8: $x = \frac{4}{8} = \frac{1}{2}$

Step 3: The value $x = \frac{1}{2}$ is where the denominator becomes zero, so this value is excluded from the domain.

Therefore, the domain of the function is all real numbers except $x = \frac{1}{2}$.

The domain of the function is $\boxed{x \ne \frac{1}{2}}$.