1. **State the problem:** Subtract the rational expressions $$\frac{9x^2 + 3}{14x^2 - 9} - \frac{-3x^2 + 11}{14x^2 - 9}$$. 2. **Identify the common denominator:** Both expressions have the same denominator $$14x^2 - 9$$. 3. **Subtract the numerators:** Since denominators are the same, subtract the numerators directly: $$\frac{(9x^2 + 3) - (-3x^2 + 11)}{14x^2 - 9}$$ 4. **Simplify the numerator:** $$9x^2 + 3 + 3x^2 - 11 = (9x^2 + 3x^2) + (3 - 11) = 12x^2 - 8$$ 5. **Rewrite the expression:** $$\frac{12x^2 - 8}{14x^2 - 9}$$ 6. **Factor numerator and denominator if possible:** - Numerator: $$12x^2 - 8 = 4(3x^2 - 2)$$ - Denominator: $$14x^2 - 9$$ cannot be factored easily over integers. 7. **Final simplified form:** $$\frac{4(3x^2 - 2)}{14x^2 - 9}$$ This is the simplified result of the subtraction.