Question

Add the following rational expressions. (1 point) Item 1 2x+3 x+2 + x-2 x+2

Answer 1

To add the rational expressions \(\frac{2x + 3}{x + 2} + \frac{x - 2}{x + 2}\), we can follow these steps:

1. **Combine the fractions**: Since both fractions have the same denominator \((x + 2)\), we can combine them into a single fraction:
\[
\frac{2x + 3 + (x - 2)}{x + 2}
\]

2. **Simplify the numerator**: Next, we simplify the numerator:
\[
2x + 3 + x - 2 = 3x + 1
\]

3. **Write the combined fraction**:
\[
\frac{3x + 1}{x + 2}
\]

So, the sum of the given rational expressions is:
\[
\frac{3x + 1}{x + 2}
\]