1. **State the problem:** Solve the equation $$\frac{x^2 - 3x + 2}{x - 1} = 0$$ for $x$. 2. **Recall the rule:** A fraction equals zero if and only if its numerator is zero and the denominator is not zero. 3. **Set the numerator equal to zero:** $$x^2 - 3x + 2 = 0$$ 4. **Factor the quadratic:** $$x^2 - 3x + 2 = (x - 1)(x - 2)$$ 5. **Solve for zeros of numerator:** $$x - 1 = 0 \Rightarrow x = 1$$ $$x - 2 = 0 \Rightarrow x = 2$$ 6. **Check denominator for restrictions:** Denominator is $x - 1$, so $x \neq 1$ to avoid division by zero. 7. **Exclude $x=1$ because it makes denominator zero.** 8. **Final solution:** $$x = 2$$ **Answer:** The solution to the equation is $x = 2$. Among the multiple-choice options, the correct answer is **a. 2**.