1. **State the problem:** Simplify the expression $$\frac{7y - 5}{12y} - \frac{10y - 19}{12y} + \frac{10 - 15y}{12y}$$ given that $y \neq 0$. 2. **Identify the common denominator:** All fractions have the same denominator $12y$, so we can combine the numerators directly over this denominator. 3. **Combine the numerators:** $$\frac{7y - 5 - (10y - 19) + (10 - 15y)}{12y}$$ 4. **Distribute the minus sign in the second numerator:** $$\frac{7y - 5 - 10y + 19 + 10 - 15y}{12y}$$ 5. **Combine like terms in the numerator:** - Combine $y$ terms: $7y - 10y - 15y = (7 - 10 - 15)y = -18y$ - Combine constants: $-5 + 19 + 10 = 24$ So numerator becomes: $$-18y + 24$$ 6. **Write the simplified fraction:** $$\frac{-18y + 24}{12y}$$ 7. **Factor numerator and denominator:** $$\frac{-6(3y - 4)}{12y}$$ 8. **Simplify the fraction by canceling common factors:** $$\frac{\cancel{-6}(3y - 4)}{\cancel{12}y} = \frac{-6(3y - 4)}{12y} = \frac{-6}{12} \cdot \frac{3y - 4}{y} = -\frac{1}{2} \cdot \frac{3y - 4}{y} = -\frac{3y - 4}{2y}$$ 9. **Final simplified expression:** $$-\frac{3y - 4}{2y}$$ **Note:** $y \neq 0$ to avoid division by zero.