Question
Add the following rational expressions:
2x+3/x+2 + x-2/x+2
2x+3/x+2 + x-2/x+2
Answers
GPT-4o mini
To add the rational expressions \(\frac{2x+3}{x+2} + \frac{x-2}{x+2}\), you can follow these steps:
1. Since both expressions have the same denominator \((x + 2)\), you can combine 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. So, we can rewrite the expression as:
\[
\frac{3x + 1}{x + 2}
\]
Thus, the sum of the rational expressions is:
\[
\frac{3x + 1}{x + 2}
\]
1. Since both expressions have the same denominator \((x + 2)\), you can combine 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. So, we can rewrite the expression as:
\[
\frac{3x + 1}{x + 2}
\]
Thus, the sum of the rational expressions is:
\[
\frac{3x + 1}{x + 2}
\]