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