1. **State the problem:** We need to evaluate the limit $$\lim_{x \to 2^-} \frac{x^2 - 4x + 3}{x - 1}$$ which means finding the value the expression approaches as $x$ approaches 2 from the left side. 2. **Recall the formula and rules:** The limit of a rational function as $x$ approaches a point can often be found by direct substitution if the function is defined there. If direct substitution leads to an indeterminate form like $\frac{0}{0}$, we simplify the expression first. 3. **Simplify the numerator:** Factor the quadratic expression: $$x^2 - 4x + 3 = (x - 1)(x - 3)$$ 4. **Rewrite the expression:** $$\frac{x^2 - 4x + 3}{x - 1} = \frac{(x - 1)(x - 3)}{x - 1}$$ 5. **Cancel common factors:** For $x \neq 1$, the $(x - 1)$ terms cancel out: $$= x - 3$$ 6. **Evaluate the limit:** Now substitute $x = 2$ from the left side: $$\lim_{x \to 2^-} (x - 3) = 2 - 3 = -1$$ 7. **Conclusion:** The limit is $-1$. **Final answer:** b. -1