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 - not selected, this is the correct answer
Score
explain how you get get that answer
To find the sum of rational expressions, we need to combine like terms in the numerator and denominator.
In this problem, the numerator of the sum is (x^2 - 23x - 2) + (x + 5) + (3x - 2). Simplifying the numerator,
= x^2 - 23x - 2 + x + 5 + 3x - 2
= x^2 - 19x + 1
The denominator is (x - 2) + (3x - 2). Simplifying the denominator,
= x - 2 + 3x - 2
= 4x - 4
Therefore, the sum is (x^2 - 19x + 1) / (4x - 4).
This can be simplified further, but since the answer choices don't provide simplified forms, we leave it as is.