The expression to be simplified is:

$\frac{4x + 3}{2} + \frac{4x}{2}$

Since both fractions have the same denominator (2), we can add the numerators directly:

$\frac{(4x + 3) + 4x}{2} = \frac{4x + 3 + 4x}{2} = \frac{8x + 3}{2}$

This is already in its simplest form, as the numerator $8x + 3$ cannot be factored further. Therefore, the final answer is:

$\frac{8x + 3}{2}$

Would you like further details or explanations?

Here are 5 related questions to expand this concept:

1. How would you subtract rational expressions with the same denominator?
2. How do you add rational expressions with different denominators?
3. What happens if the numerator can be factored? How would that impact simplification?
4. How do you simplify complex rational expressions with variables in both numerator and denominator?
5. How can rational expressions be applied in solving real-life problems like rates and proportions?

Tip: When adding or subtracting rational expressions, always check if the denominators are the same first; if not, find a common denominator before combining the numerators.