1. **State the problem:** Evaluate the limit $$\lim_{x \to 1^-} \frac{x^2 - 4x + 3}{x - 1}$$ as $x$ approaches 1 from the left. 2. **Recall the formula and rules:** The limit of a rational function as $x$ approaches a value can often be found by direct substitution unless it results in an indeterminate form like $\frac{0}{0}$. If so, factor and simplify the expression. 3. **Check direct substitution:** Substitute $x=1$ into numerator and denominator: $$1^2 - 4(1) + 3 = 1 - 4 + 3 = 0$$ $$1 - 1 = 0$$ This gives $\frac{0}{0}$, an indeterminate form. 4. **Factor numerator:** $$x^2 - 4x + 3 = (x - 3)(x - 1)$$ 5. **Simplify the expression:** $$\frac{(x - 3)(x - 1)}{x - 1} = x - 3, \quad x \neq 1$$ 6. **Evaluate the limit of the simplified expression as $x \to 1^-$:** $$\lim_{x \to 1^-} (x - 3) = 1 - 3 = -2$$ 7. **Interpretation:** Since the simplified function is continuous near $x=1$, the limit from the left is $-2$. **Final answer:** $-2$ (option a).