1. **State the problem:** Simplify the expression $$\frac{-2}{-3q+5} + \frac{2q-3}{1}$$. 2. **Rewrite the expression:** The expression is $$\frac{-2}{-3q+5} + (2q-3)$$. 3. **Find a common denominator:** The common denominator is $$-3q+5$$. 4. **Rewrite the second term with the common denominator:** $$2q-3 = \frac{(2q-3)(-3q+5)}{-3q+5}$$. 5. **Combine the fractions:** $$\frac{-2}{-3q+5} + \frac{(2q-3)(-3q+5)}{-3q+5} = \frac{-2 + (2q-3)(-3q+5)}{-3q+5}$$. 6. **Expand the numerator:** $$(2q-3)(-3q+5) = 2q \times -3q + 2q \times 5 - 3 \times -3q - 3 \times 5 = -6q^2 + 10q + 9q - 15 = -6q^2 + 19q - 15$$. 7. **Add the -2:** $$-2 + (-6q^2 + 19q - 15) = -6q^2 + 19q - 17$$. 8. **Final simplified expression:** $$\frac{-6q^2 + 19q - 17}{-3q + 5}$$. This is the simplified form of the original expression.