Question

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

x^3+3/3x−2
Start Fraction x cubed plus 3 over 3 x minus 2 End Fraction

x^2+x+7/3x−2
Start Fraction x squared plus x plus 7 over 3 x minus 2 End Fraction

x^2+x+3/3x−2
Start Fraction x squared plus x plus 3 over 3 x minus 2 End Fraction

x^2+x+3/6x−4
Start Fraction x squared plus x plus 3 over 6 x minus 4 End Fraction
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Answer 1

To add the two rational expressions \(\frac{x^2 - 2}{3x - 2}\) and \(\frac{x + 5}{3x - 2}\), we can combine them since they already have a common denominator.

The expression will look like this:

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

Now, we will simplify the numerator:

1. Combine terms in the numerator:

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

So, the combined expression is:

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

Thus, the sum of the rational expressions is:

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

From the options provided, this matches with:

\[
\text{Start Fraction x squared plus x plus 3 over 3 x minus 2 End Fraction}
\]

So the correct answer is:

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