1. **Problem:** Given $f(x) = 3x - 3$ and $g(x) = \frac{2}{x-1}$, find $\left(\frac{f}{g} - 2f(3)\right)$. 2. **Step 1:** Calculate $f(3)$. $$f(3) = 3(3) - 3 = 9 - 3 = 6$$ 3. **Step 2:** Write the expression $\frac{f}{g} - 2f(3)$ explicitly. $$\frac{f(x)}{g(x)} - 2f(3) = \frac{3x - 3}{\frac{2}{x-1}} - 2 \times 6 = \frac{3x - 3}{\frac{2}{x-1}} - 12$$ 4. **Step 3:** Simplify the fraction division. $$\frac{3x - 3}{\frac{2}{x-1}} = (3x - 3) \times \frac{x-1}{2} = \frac{(3x - 3)(x-1)}{2}$$ 5. **Step 4:** Factor $3x - 3$ as $3(x-1)$. $$\frac{3(x-1)(x-1)}{2} = \frac{3(x-1)^2}{2}$$ 6. **Step 5:** Substitute back into the expression. $$\frac{3(x-1)^2}{2} - 12$$ 7. **Step 6:** Evaluate at a convenient $x$ to find the value of the expression. Since the problem does not specify $x$, assume $x=3$ (used in $f(3)$). $$\frac{3(3-1)^2}{2} - 12 = \frac{3(2)^2}{2} - 12 = \frac{3 \times 4}{2} - 12 = \frac{12}{2} - 12 = 6 - 12 = -6$$ **Answer:** $-6$ which corresponds to option A.