1. **State the problem:** Simplify the expression $$9 - 45 \cdot \frac{7}{5} - \left[12 + 7 - 21 \cdot \frac{9}{3}\right]$$. 2. **Recall order of operations:** Perform multiplication and division before addition and subtraction. Also, simplify inside brackets first. 3. **Simplify inside the brackets:** $$21 \cdot \frac{9}{3} = 21 \cdot 3 = 63$$ So inside the brackets: $$12 + 7 - 63 = 19 - 63 = -44$$ 4. **Simplify the multiplication outside the brackets:** $$45 \cdot \frac{7}{5} = 45 \cdot 1.4 = 63$$ 5. **Rewrite the expression:** $$9 - 63 - (-44)$$ 6. **Simplify subtraction of a negative number:** $$9 - 63 + 44$$ 7. **Perform the operations from left to right:** $$9 - 63 = -54$$ $$-54 + 44 = -10$$ **Final answer:** $$-10$$