Question

Add the rational expressions to find the sum: x^2−2/3x−2+x+5/3x−2
.(1 point)
Responses

x2+x+33x−2
Start Fraction x squared plus x plus 3 over 3 x minus 2 End Fraction

x2+x+73x−2
Start Fraction x squared plus x plus 7 over 3 x minus 2 End Fraction

x2+x+36x−4
Start Fraction x squared plus x plus 3 over 6 x minus 4 End Fraction

x3+33x−2

Answer 1

To add the rational expressions \(\frac{x^2 - 2}{3x - 2} + \frac{x + 5}{3x - 2}\), we can follow these steps:

1. Since both fractions have a common denominator of \(3x - 2\), we can combine the numerators directly:

\[
\frac{x^2 - 2 + (x + 5)}{3x - 2}
\]

2. Simplify the numerator:

\[
x^2 - 2 + x + 5 = x^2 + x + 3
\]

3. The combined expression is:

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

From the provided responses, the correct answer is:

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

So, the correct response is:

**x² + x + 3 / (3x - 2)**