1. **State the problem:** Simplify the expression $$\frac{x^2 + 3x}{x + 10} - \frac{3x + 100}{x + 10}$$. 2. **Identify the formula and rules:** Since both fractions have the same denominator, we can combine the numerators over the common denominator: $$\frac{A}{C} - \frac{B}{C} = \frac{A - B}{C}$$ 3. **Apply the rule:** $$\frac{x^2 + 3x}{x + 10} - \frac{3x + 100}{x + 10} = \frac{(x^2 + 3x) - (3x + 100)}{x + 10}$$ 4. **Simplify the numerator:** $$x^2 + 3x - 3x - 100 = x^2 - 100$$ 5. **Rewrite the expression:** $$\frac{x^2 - 100}{x + 10}$$ 6. **Factor the numerator:** Recognize that $$x^2 - 100$$ is a difference of squares: $$x^2 - 10^2 = (x - 10)(x + 10)$$ 7. **Simplify the fraction:** $$\frac{(x - 10)(x + 10)}{x + 10}$$ Since $$x + 10 \neq 0$$, we can cancel $$x + 10$$: $$x - 10$$ **Final answer:** $$x - 10$$