Question
What is the correct answer: Add the rational expressions to find the sum: x2-2/3x-2 +x+5/3x-2
Answers
GPT-4o mini
To add the rational expressions \(\frac{x^2 - 2}{3x - 2} + \frac{x + 5}{3x - 2}\), we start by recognizing that both expressions have the same denominator. This means we can combine the numerators directly over the common denominator.
1. **Combine the numerators**:
\[
\frac{x^2 - 2 + (x + 5)}{3x - 2}
\]
2. **Simplify the numerator**:
The numerator is:
\[
x^2 - 2 + x + 5 = x^2 + x + 3
\]
So, we rewrite the expression as:
\[
\frac{x^2 + x + 3}{3x - 2}
\]
3. **Final result**:
The sum of the rational expressions is:
\[
\frac{x^2 + x + 3}{3x - 2}
\]
This is the simplified expression representing the sum of the original rational expressions.
1. **Combine the numerators**:
\[
\frac{x^2 - 2 + (x + 5)}{3x - 2}
\]
2. **Simplify the numerator**:
The numerator is:
\[
x^2 - 2 + x + 5 = x^2 + x + 3
\]
So, we rewrite the expression as:
\[
\frac{x^2 + x + 3}{3x - 2}
\]
3. **Final result**:
The sum of the rational expressions is:
\[
\frac{x^2 + x + 3}{3x - 2}
\]
This is the simplified expression representing the sum of the original rational expressions.