1. **State the problem:** Evaluate the limit $$\lim_{x \to 1} \frac{x^2 - 2x + 7}{2x^2 - 3x - 4}$$ using limit laws. 2. **Recall limit laws:** If the limit of numerator and denominator exist and denominator limit is not zero, then $$\lim_{x \to a} \frac{f(x)}{g(x)} = \frac{\lim_{x \to a} f(x)}{\lim_{x \to a} g(x)}$$. 3. **Evaluate numerator at $x=1$: $$1^2 - 2(1) + 7 = 1 - 2 + 7 = 6$$**. 4. **Evaluate denominator at $x=1$: $$2(1)^2 - 3(1) - 4 = 2 - 3 - 4 = -5$$**. 5. **Since denominator limit is not zero, apply limit law:** $$\lim_{x \to 1} \frac{x^2 - 2x + 7}{2x^2 - 3x - 4} = \frac{6}{-5} = -\frac{6}{5}$$. **Final answer:** $$-\frac{6}{5}$$