Add the rational expressions to find the sum: x2−23x−2+x+53x−2. Responses x3+33x−2 the fraction with numerator x cubed plus 3 and denominator 3 x minus 2 - no response given x2+x+73x−2 the fraction with numerator x squared plus x plus 7 and denominator 3 x minus 2 - no response given x2+x+36x−4 the fraction with numerator x squared plus x plus 3 and denominator 6 x minus 4 - incorrect x2+x+33x−2 the fraction with numerator x squared plus x plus 3 and denominator 3 x minus 2 -this is the correct answer Score. explain how you would get this answer x2+x+33x−2 has the correct answer.
To find the sum of the rational expressions x^2 - 23x - 2 and x + 5/3x - 2, we need to find a common denominator for both fractions then add the numerators.
The common denominator is (3x - 2).
For the first fraction, (x^2 - 23x - 2), we don't need to make any changes to the numerator.
For the second fraction, we can rewrite it as (3x + 5)/(3x - 2) to have the common denominator.
Now we can add the numerators:
(x^2 - 23x - 2) + (3x + 5) = x^2 - 23x + 3x - 2 + 5 = x^2 - 20x + 3
Thus, the sum of the rational expressions is x^2 - 20x + 3 divided by (3x - 2), which can be written as (x^2 + x + 3)/(3x - 2).