1. **State the problem:** We need to evaluate the limit of the function $$\frac{x^2 - 4x + 3}{x - 1}$$ as $$x$$ approaches 6. 2. **Recall the formula and rules:** The limit of a rational function as $$x$$ approaches a value can often be found by direct substitution, provided the denominator is not zero at that point. 3. **Check the denominator at $$x=6$$:** $$6 - 1 = 5 \neq 0$$, so direct substitution is valid. 4. **Evaluate numerator at $$x=6$$:** $$6^2 - 4 \times 6 + 3 = 36 - 24 + 3 = 15$$. 5. **Evaluate denominator at $$x=6$$:** $$6 - 1 = 5$$. 6. **Calculate the limit:** $$\frac{15}{5} = 3$$. **Final answer:** The limit as $$x$$ approaches 6 is **3**.