Question
Add the rational expressions to find the sum: 2/x+3/x+5
(1 point)
Responses
13x+5
the fraction with numerator 13 and denominator x plus 5
2x+8x2+5x
the fraction with numerator 2 x plus 8 and denominator x squared plus 5 x
5x+10x2+5x
the fraction with numerator 5 x plus 10 and denominator x squared plus 5 x
52x+5
(1 point)
Responses
13x+5
the fraction with numerator 13 and denominator x plus 5
2x+8x2+5x
the fraction with numerator 2 x plus 8 and denominator x squared plus 5 x
5x+10x2+5x
the fraction with numerator 5 x plus 10 and denominator x squared plus 5 x
52x+5
Answers
GPT-4o mini
To add the rational expressions \( \frac{2}{x} + \frac{3}{x} + 5 \), we start by finding a common denominator.
The two fractions \( \frac{2}{x} \) and \( \frac{3}{x} \) already have a common denominator of \( x \). We can combine them:
\[
\frac{2 + 3}{x} = \frac{5}{x}
\]
Now, we can add the integer 5 (which can be rewritten as \( \frac{5x}{x} \) for common denominators):
\[
\frac{5}{x} + 5 = \frac{5}{x} + \frac{5x}{x} = \frac{5 + 5x}{x} = \frac{5x + 5}{x}
\]
Thus, the sum of the rational expressions is:
\[
\frac{5x + 5}{x}
\]
Looking at your response options, the correct expression is:
**5x + 10/x + 5** (choice 3 can be considered equivalent to a form of our answer).
However, to fit it to the exact form if we are considering integer separation, none of the provided options directly match this. There might be an error in representation. Please clarify or check options against the derived sum if this answer doesn’t appear as expected.
The two fractions \( \frac{2}{x} \) and \( \frac{3}{x} \) already have a common denominator of \( x \). We can combine them:
\[
\frac{2 + 3}{x} = \frac{5}{x}
\]
Now, we can add the integer 5 (which can be rewritten as \( \frac{5x}{x} \) for common denominators):
\[
\frac{5}{x} + 5 = \frac{5}{x} + \frac{5x}{x} = \frac{5 + 5x}{x} = \frac{5x + 5}{x}
\]
Thus, the sum of the rational expressions is:
\[
\frac{5x + 5}{x}
\]
Looking at your response options, the correct expression is:
**5x + 10/x + 5** (choice 3 can be considered equivalent to a form of our answer).
However, to fit it to the exact form if we are considering integer separation, none of the provided options directly match this. There might be an error in representation. Please clarify or check options against the derived sum if this answer doesn’t appear as expected.