Question
Find the sum: \( \frac{x-2}{x^{2}+1}+\frac{x+3}{x^{2}+1} \)
Ask by Simmons Stewart. in the United States
Mar 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The sum is \( \frac{2x+1}{x^2+1} \).
Solution
1. Write the sum with a common denominator:
\[
\frac{x-2}{x^2+1} + \frac{x+3}{x^2+1} = \frac{(x-2)+(x+3)}{x^2+1}
\]
2. Combine like terms in the numerator:
\[
(x-2)+(x+3) = x + x + (-2+3) = 2x + 1
\]
3. Write the simplified expression:
\[
\frac{2x+1}{x^2+1}
\]
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Simplify this solution Mind Expander
To find the sum of the fractions \( \frac{x-2}{x^2+1} + \frac{x+3}{x^2+1} \), we can start by combining the two fractions. Since they have a common denominator, we can add the numerators directly: \[ \frac{(x-2) + (x+3)}{x^2+1} \] Now, simplify the numerator: \[ (x-2) + (x+3) = x - 2 + x + 3 = 2x + 1 \] Thus, the sum can be simplified to: \[ \frac{2x + 1}{x^2 + 1} \] So the final result is: \[ \frac{2x + 1}{x^2 + 1} \]
