1. **State the problem:** We are given two functions $g(x) = 4x - 4$ and $f(x) = x + 4$. We need to find the function $\left(\frac{g}{f}\right)(x)$, which means dividing $g(x)$ by $f(x)$. 2. **Write the formula:** The division of two functions is given by $$\left(\frac{g}{f}\right)(x) = \frac{g(x)}{f(x)}$$ 3. **Substitute the given functions:** $$\left(\frac{g}{f}\right)(x) = \frac{4x - 4}{x + 4}$$ 4. **Simplify the numerator:** Factor out the common factor 4: $$\frac{4x - 4}{x + 4} = \frac{4(x - 1)}{x + 4}$$ 5. **State restrictions:** Since division by zero is undefined, the denominator cannot be zero: $$x + 4 \neq 0 \implies x \neq -4$$ 6. **Final answer:** $$\boxed{\left(\frac{g}{f}\right)(x) = \frac{4(x - 1)}{x + 4}, \quad x \neq -4}$$ This means the function $\left(\frac{g}{f}\right)(x)$ is defined for all real numbers except $x = -4$ where the denominator is zero.