Add the rational expressions to find the sum: x2−23x−2+x+53x−2.

Question

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

Answer 1

To find the sum of the rational expressions, we need to combine like terms. In this case, we have x^2 terms, x terms, and constant terms.

Starting with the x^2 terms, we have x^2 - 23x - 2 + 0x^2 + 0x + 0 = x^2 - 23x - 2.

Moving on to the x terms, we have 0x^2 + 1x + 53x - 2 = 54x - 2.

Finally, we have the constant terms, which are -2 + 0 = -2.

Combining all these terms together, we get the sum x^2 - 23x - 2 + 54x - 2 = x^2 + 31x - 4.

Therefore, the correct answer is the fraction with numerator x squared plus x plus 33 and denominator 3x minus 2.