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 the correct answer
To find the sum of rational expressions, you need to first combine like terms in both the numerator and denominator.
In this case, the numerators are x^2 - 23x - 2 and x + 5(3x - 2).
Combining like terms in the numerator, we get:
x^2 - 23x - 2 + 3x + 5(-2) = x^2 - 23x - 2 + 3x - 10 = x^2 - 20x - 12
Combining like terms in the denominator, we get: 3x - 2
So, the final rational expression is:
(x^2 - 20x - 12)/(3x - 2)