To add the rational expressions \(\frac{2x + 3}{x + 2}\) and \(\frac{x - 2}{x + 2}\), we can combine them since they have the same denominator:
\[ \frac{2x + 3}{x + 2} + \frac{x - 2}{x + 2} = \frac{(2x + 3) + (x - 2)}{x + 2} \]
Now, combine the numerators:
\[ 2x + 3 + x - 2 = (2x + x) + (3 - 2) = 3x + 1 \]
So we have:
\[ \frac{3x + 1}{x + 2} \]
This means the sum of the given rational expressions is:
\[ \frac{3x + 1}{x + 2} \]
This is your final answer.