Find the sum:

[tex]\[ \frac{x-2}{x^2+1} + \frac{x+3}{x^2+1} \][/tex]

A. [tex]\(\frac{2x+1}{2x^2+2}\)[/tex]

B. [tex]\(\frac{1}{x^2+1}\)[/tex]

C. [tex]\(\frac{2x+1}{x^2+1}\)[/tex]

D. [tex]\(\frac{2}{x}\)[/tex]



Answer :

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]