1. **State the problem:** Simplify the rational function $$\frac{x^2 + x - 6}{x^2 - 7x + 10}$$. 2. **Recall the formula and rules:** To simplify a rational function, factor both numerator and denominator completely and then cancel any common factors. 3. **Factor the numerator:** $$x^2 + x - 6 = (x + 3)(x - 2)$$ 4. **Factor the denominator:** $$x^2 - 7x + 10 = (x - 5)(x - 2)$$ 5. **Write the expression with factors:** $$\frac{(x + 3)(x - 2)}{(x - 5)(x - 2)}$$ 6. **Cancel the common factor $(x - 2)$:** $$\frac{(x + 3)\cancel{(x - 2)}}{(x - 5)\cancel{(x - 2)}}$$ 7. **Final simplified form:** $$\frac{x + 3}{x - 5}$$ **Answer:** The simplified rational function is $$\frac{x + 3}{x - 5}$$.