1. **State the problem:** Simplify the expression $$\frac{3}{2x + 5} - \frac{5}{3x + 2}$$. 2. **Find a common denominator:** The denominators are $2x + 5$ and $3x + 2$. The common denominator is their product: $$(2x + 5)(3x + 2)$$. 3. **Rewrite each fraction with the common denominator:** $$\frac{3}{2x + 5} = \frac{3(3x + 2)}{(2x + 5)(3x + 2)}$$ $$\frac{5}{3x + 2} = \frac{5(2x + 5)}{(2x + 5)(3x + 2)}$$ 4. **Subtract the numerators:** $$\frac{3(3x + 2) - 5(2x + 5)}{(2x + 5)(3x + 2)}$$ 5. **Expand the numerators:** $$3(3x + 2) = 9x + 6$$ $$5(2x + 5) = 10x + 25$$ 6. **Perform the subtraction:** $$9x + 6 - (10x + 25) = 9x + 6 - 10x - 25 = (9x - 10x) + (6 - 25) = -x - 19$$ 7. **Write the simplified expression:** $$\frac{-x - 19}{(2x + 5)(3x + 2)}$$ 8. **Factor out the negative sign in the numerator:** $$\frac{-(x + 19)}{(2x + 5)(3x + 2)}$$ **Final answer:** $$\boxed{\frac{-(x + 19)}{(2x + 5)(3x + 2)}}$$