Question

Add the following rational expressions.
2x+3/x+2 + x-2/x+2

Answer 1

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.