Question
Add the rational expressions to find the sum: 5x−3/x+1+x+2/x+1 (1 point) Responses 6x+52x+2 the fraction with numerator 6 x plus 5 and denominator 2 x plus 2 6x−1x+1 the fraction with numerator 6 x minus 1 and denominator x plus 1 6x−12x+2 the fraction with numerator 6 x minus 1 and denominator 2 x plus 2 6x+5x+1
Answers
GPT-4o mini
To add the rational expressions \( \frac{5x - 3}{x + 1} + \frac{x + 2}{x + 1} \), we need to combine them over a common denominator.
Since both fractions have the same denominator \( x + 1 \), we can simply add their numerators:
\[
\frac{5x - 3 + (x + 2)}{x + 1}
\]
Now, combine the terms in the numerator:
\[
5x - 3 + x + 2 = (5x + x) + (-3 + 2) = 6x - 1
\]
So, we have:
\[
\frac{6x - 1}{x + 1}
\]
Thus, the sum of the given rational expressions is:
\[
\frac{6x - 1}{x + 1}
\]
From the options provided, the correct response is:
**6x−1/x+1** (the fraction with numerator \( 6x - 1 \) and denominator \( x + 1 \)).
Since both fractions have the same denominator \( x + 1 \), we can simply add their numerators:
\[
\frac{5x - 3 + (x + 2)}{x + 1}
\]
Now, combine the terms in the numerator:
\[
5x - 3 + x + 2 = (5x + x) + (-3 + 2) = 6x - 1
\]
So, we have:
\[
\frac{6x - 1}{x + 1}
\]
Thus, the sum of the given rational expressions is:
\[
\frac{6x - 1}{x + 1}
\]
From the options provided, the correct response is:
**6x−1/x+1** (the fraction with numerator \( 6x - 1 \) and denominator \( x + 1 \)).