1. **State the problem:** Simplify the algebraic expression $$\frac{2}{-3q+5} + 2q - 3$$. 2. **Rewrite the expression:** The expression is $$\frac{2}{-3q+5} + 2q - 3$$. 3. **Note:** The term $$\frac{2}{-3q+5}$$ is a fraction and cannot be combined directly with the polynomial terms $$2q - 3$$ without a common denominator. 4. **Express the polynomial terms with the common denominator:** Multiply $$2q - 3$$ by $$\frac{-3q+5}{-3q+5}$$ to get a common denominator: $$\frac{2}{-3q+5} + \frac{(2q - 3)(-3q + 5)}{-3q + 5}$$ 5. **Expand the numerator of the second fraction:** $$(2q)(-3q) + (2q)(5) + (-3)(-3q) + (-3)(5) = -6q^2 + 10q + 9q - 15 = -6q^2 + 19q - 15$$ 6. **Combine the fractions:** $$\frac{2 + (-6q^2 + 19q - 15)}{-3q + 5} = \frac{-6q^2 + 19q - 13}{-3q + 5}$$ 7. **Final simplified expression:** $$\boxed{\frac{-6q^2 + 19q - 13}{-3q + 5}}$$ This is the simplified form of the original expression.