Question

What is the correct answer: Add the rational expressions to find the sum: x2-2/3x-2 +x+5/3x-2

x2+x+7/3x-2
x2+x+3/6x-4
x2+x+3/3x-2
x3+3/3x-2

Answer 1

To add the rational expressions \(\frac{x^2 - 2}{3x - 2}\) and \(\frac{x + 5}{3x - 2}\), we start by observing that they have a common denominator, \(3x - 2\).

The sum can be written as:

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

Now we combine the numerators:

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

So the expression becomes:

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

Thus, the sum of the rational expressions is:

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

Now, looking at the given options:

1. \( \frac{x^2 + x + 7}{3x - 2} \)
2. \( \frac{x^2 + x + 3}{6x - 4} \)
3. \( \frac{x^2 + x + 3}{3x - 2} \)
4. \( \frac{x^3 + 3}{3x - 2} \)

The correct answer is:

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

which is option 3.