1. **State the problem:** Write the expression $$\frac{3}{2x-1} - \frac{2}{x+3}$$ as a single fraction, given that $$x \neq \frac{1}{2}$$ and $$x \neq -3$$. 2. **Formula and rules:** To combine fractions with different denominators, find the least common denominator (LCD) and rewrite each fraction with the LCD as the denominator. 3. **Find the LCD:** The denominators are $$2x-1$$ and $$x+3$$, so the LCD is $$(2x-1)(x+3)$$. 4. **Rewrite each fraction:** $$\frac{3}{2x-1} = \frac{3(x+3)}{(2x-1)(x+3)}$$ $$\frac{2}{x+3} = \frac{2(2x-1)}{(2x-1)(x+3)}$$ 5. **Subtract the fractions:** $$\frac{3(x+3)}{(2x-1)(x+3)} - \frac{2(2x-1)}{(2x-1)(x+3)} = \frac{3(x+3) - 2(2x-1)}{(2x-1)(x+3)}$$ 6. **Expand the numerators:** $$3(x+3) = 3x + 9$$ $$2(2x-1) = 4x - 2$$ 7. **Substitute and simplify numerator:** $$3x + 9 - (4x - 2) = 3x + 9 - 4x + 2 = (3x - 4x) + (9 + 2) = -x + 11$$ 8. **Final expression:** $$\frac{-x + 11}{(2x-1)(x+3)}$$ This is the single fraction form of the original expression.