Determine the Domain of the Fraction Function: 4x+4 Over x - 1/8

To find the domain of the function $\frac{4x+4}{x-\frac{1}{8}}$, we need to determine when the denominator equals zero because division by zero is undefined.

Step-by-step approach:

• Step 1: Identify the denominator of the function: $x - \frac{1}{8}$.
• Step 2: Set the denominator equal to zero to find the values of $x$ to exclude: $x - \frac{1}{8} = 0$.
• Step 3: Solve the equation for $x$:
  $x = \frac{1}{8}$.

This means the function is undefined when $x = \frac{1}{8}$. Thus, the domain of the function consists of all real numbers except $x = \frac{1}{8}$.

The domain of the function is therefore all $x$ such that:

$x \ne \frac{1}{8}$

Referring to the answer choices, the correct choice is:

$x\ne\frac{1}{8}$