1. **State the problem:** Write the expression $$\frac{4x + 1}{2} + \frac{2x - 1}{3}$$ as a single fraction in simplest form. 2. **Find a common denominator:** The denominators are 2 and 3. The least common denominator (LCD) is $$6$$. 3. **Rewrite each fraction with the LCD:** $$\frac{4x + 1}{2} = \frac{(4x + 1) \times 3}{2 \times 3} = \frac{3(4x + 1)}{6} = \frac{12x + 3}{6}$$ $$\frac{2x - 1}{3} = \frac{(2x - 1) \times 2}{3 \times 2} = \frac{2(2x - 1)}{6} = \frac{4x - 2}{6}$$ 4. **Add the fractions:** $$\frac{12x + 3}{6} + \frac{4x - 2}{6} = \frac{(12x + 3) + (4x - 2)}{6} = \frac{12x + 3 + 4x - 2}{6} = \frac{16x + 1}{6}$$ 5. **Simplify the numerator if possible:** The numerator is $$16x + 1$$, which cannot be simplified further. 6. **Final answer:** $$\frac{16x + 1}{6}$$ Note: The answer you provided, $$16x + 5$$, is not equivalent to the sum of the fractions.