Question
Add the rational expressions to find the sum: 2/x+3/x+5 (1 point) Responses 52x+5 the fraction with numerator 5 and denominator 2 x plus 5 5x+10x2+5x the fraction with numerator 5 x plus 10 and denominator x squared plus 5 x 2x+8x2+5x the fraction with numerator 2 x plus 8 and denominator x squared plus 5 x 13x+5
Answers
GPT-4o mini
To find the sum of the rational expressions \( \frac{2}{x} + \frac{3}{x} + 5 \), we first need to combine the fractions that have the same denominator.
1. Combine \( \frac{2}{x} + \frac{3}{x} \):
\[
\frac{2}{x} + \frac{3}{x} = \frac{2 + 3}{x} = \frac{5}{x}
\]
2. Now add \( \frac{5}{x} + 5 \). We can rewrite the whole number \( 5 \) as a fraction with the same denominator \( x \):
\[
5 = \frac{5x}{x}
\]
3. So now we have:
\[
\frac{5}{x} + \frac{5x}{x} = \frac{5 + 5x}{x} = \frac{5x + 5}{x}
\]
Thus, the final expression for the sum is:
\[
\frac{5x + 5}{x}
\]
Among the choices provided, this corresponds to:
**5x + 10/x² + 5x** (if this matches and denotes \( \frac{5x + 10}{x^2 + 5x} \)), though your question presented options in a slightly different format, this could possibly relate depending on interpretations of coefficients and simplifications.
If you meant to look for simplifications just for \( 5x + 10 \), it comes from \( \frac{5x + 5}{x}\) and doesn’t explicitly relate directly to \( 5x + 10 \).
If that doesn't fit with the original choices, typically these problems might only expand rational formats.
To summarize, combine fractions correctly and it leads to:
**Final Answer:** \( \frac{5x + 5}{x} \) or equivalent depending on preference.
1. Combine \( \frac{2}{x} + \frac{3}{x} \):
\[
\frac{2}{x} + \frac{3}{x} = \frac{2 + 3}{x} = \frac{5}{x}
\]
2. Now add \( \frac{5}{x} + 5 \). We can rewrite the whole number \( 5 \) as a fraction with the same denominator \( x \):
\[
5 = \frac{5x}{x}
\]
3. So now we have:
\[
\frac{5}{x} + \frac{5x}{x} = \frac{5 + 5x}{x} = \frac{5x + 5}{x}
\]
Thus, the final expression for the sum is:
\[
\frac{5x + 5}{x}
\]
Among the choices provided, this corresponds to:
**5x + 10/x² + 5x** (if this matches and denotes \( \frac{5x + 10}{x^2 + 5x} \)), though your question presented options in a slightly different format, this could possibly relate depending on interpretations of coefficients and simplifications.
If you meant to look for simplifications just for \( 5x + 10 \), it comes from \( \frac{5x + 5}{x}\) and doesn’t explicitly relate directly to \( 5x + 10 \).
If that doesn't fit with the original choices, typically these problems might only expand rational formats.
To summarize, combine fractions correctly and it leads to:
**Final Answer:** \( \frac{5x + 5}{x} \) or equivalent depending on preference.