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 \(\frac{2x+3}{x+2} + \frac{x-2}{x+2}\), follow these steps:

1. Since both fractions have the same denominator (\(x + 2\)), you can add the numerators directly:

\[
\frac{2x + 3 + (x - 2)}{x + 2}
\]

2. Combine the numerators:

\[
2x + 3 + x - 2 = (2x + x) + (3 - 2) = 3x + 1
\]

3. Now, write the combined fraction:

\[
\frac{3x + 1}{x + 2}
\]

So, the sum of the rational expressions is:

\[
\frac{3x + 1}{x + 2}
\]