1. **State the problem:** Simplify the expression $$\frac{9(x-5)-2(y-3)}{6-3}+A$$. 2. **Apply the distributive property:** Multiply inside the parentheses: $$9(x-5) = 9x - 45$$ $$-2(y-3) = -2y + 6$$ 3. **Rewrite the numerator:** $$9x - 45 - 2y + 6 = 9x - 2y - 39$$ 4. **Simplify the denominator:** $$6 - 3 = 3$$ 5. **Rewrite the entire expression:** $$\frac{9x - 2y - 39}{3} + A$$ 6. **Divide each term in the numerator by 3:** $$\frac{9x}{3} - \frac{2y}{3} - \frac{39}{3} + A = 3x - \frac{2y}{3} - 13 + A$$ 7. **Final simplified expression:** $$3x - \frac{2y}{3} - 13 + A$$ This is the simplified form of the given expression.