Question
Add the rational expressions to find the sum: 5x+2+6x−3
.(1 point)
Responses
11x+27x2−x−6
Start Fraction 11 x plus 27 over x squared minus x minus 6 End Fraction
11x−1
Start Fraction 11 over x minus 1 End Fraction
11x−3x2−x−6
Start Fraction 11 x minus 3 over x squared minus x minus 6 End Fraction
−3x−6
.(1 point)
Responses
11x+27x2−x−6
Start Fraction 11 x plus 27 over x squared minus x minus 6 End Fraction
11x−1
Start Fraction 11 over x minus 1 End Fraction
11x−3x2−x−6
Start Fraction 11 x minus 3 over x squared minus x minus 6 End Fraction
−3x−6
Answers
GPT-4o mini
To find the sum of the rational expressions \( \frac{5x + 2}{1} + \frac{6x - 3}{1} \), we first combine the numerators over a common denominator.
1. Combine the numerators:
\[
(5x + 2) + (6x - 3) = 5x + 2 + 6x - 3 = 11x - 1
\]
2. The denominator remains \( 1 \) since both fractions have the same denominator.
Thus, the combined expression is:
\[
\frac{11x - 1}{1} = 11x - 1
\]
Now, we write it in the form of a proper fraction if needed, but here \( 11x - 1 \) is sufficient.
From the provided options, the correct choice is:
**11x−1 (Start Fraction 11 over x minus 1 End Fraction)**.
(Note: The way it is presented "Start Fraction 11 over x minus 1 End Fraction" may suggest a misunderstanding in representation. In simplest terms, it should read \( 11x - 1 \) which is just expressing \( 11x - 1 \) as a rational expression.)
However, none of the options actually reflect \( 11x - 1 \) directly as a rational form unless we interpret "Start Fraction 11 over x minus 1 End Fraction" as an incorrect formatting. The simplest result here remains \( 11x - 1 \).
1. Combine the numerators:
\[
(5x + 2) + (6x - 3) = 5x + 2 + 6x - 3 = 11x - 1
\]
2. The denominator remains \( 1 \) since both fractions have the same denominator.
Thus, the combined expression is:
\[
\frac{11x - 1}{1} = 11x - 1
\]
Now, we write it in the form of a proper fraction if needed, but here \( 11x - 1 \) is sufficient.
From the provided options, the correct choice is:
**11x−1 (Start Fraction 11 over x minus 1 End Fraction)**.
(Note: The way it is presented "Start Fraction 11 over x minus 1 End Fraction" may suggest a misunderstanding in representation. In simplest terms, it should read \( 11x - 1 \) which is just expressing \( 11x - 1 \) as a rational expression.)
However, none of the options actually reflect \( 11x - 1 \) directly as a rational form unless we interpret "Start Fraction 11 over x minus 1 End Fraction" as an incorrect formatting. The simplest result here remains \( 11x - 1 \).