To find the sum:
[tex]\[
\frac{x-2}{x^2+1}+\frac{x+3}{x^2+1}
\][/tex]
we start by noting that the denominators of both fractions are the same, which allows us to combine the numerators directly. Here’s the detailed solution:
1. Express the sum of the fractions:
[tex]\[
\frac{x-2}{x^2+1}+\frac{x+3}{x^2+1} = \frac{(x-2) + (x+3)}{x^2+1}
\][/tex]
2. Combine the numerators:
[tex]\[
(x-2) + (x+3) = x - 2 + x + 3 = 2x + 1
\][/tex]
3. Write the combined fraction:
[tex]\[
\frac{2x + 1}{x^2 + 1}
\][/tex]
So, the sum of the given expressions is:
[tex]\[
\frac{2x + 1}{x^2 + 1}
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{\frac{2x + 1}{x^2 + 1}}
\][/tex]
