Question
Add the rational expressions to find the sum: 2/x+3/x+5
.(1 point)
Responses
13x+5
Start Fraction 13 over x plus 5 End Fraction
52x+5
Start Fraction 5 over 2 x plus 5 End Fraction
5x+10x2+5x
Start Fraction 5 x plus 10 over x squared plus 5 x End Fraction
2x+8x2+5x
.(1 point)
Responses
13x+5
Start Fraction 13 over x plus 5 End Fraction
52x+5
Start Fraction 5 over 2 x plus 5 End Fraction
5x+10x2+5x
Start Fraction 5 x plus 10 over x squared plus 5 x End Fraction
2x+8x2+5x
Answers
GPT-4o mini
To find the sum of the rational expressions \( \frac{2}{x} + \frac{3}{x} + 5 \), we first need to express \( 5 \) as a fraction with a common denominator. The least common denominator here is \( x \).
1. Convert \( 5 \) into a fraction:
\[
5 = \frac{5x}{x}
\]
2. Now, we can combine the expressions:
\[
\frac{2}{x} + \frac{3}{x} + \frac{5x}{x} = \frac{2 + 3 + 5x}{x}
\]
\[
= \frac{5x + 5}{x}
\]
3. The expression can also be factored:
\[
= \frac{5(x + 1)}{x}
\]
Thus, the final result, in terms of a single rational expression, is \( \frac{5(x + 1)}{x} \).
From the options provided, none of them correctly represent the simplified sum \( \frac{5(x + 1)}{x} \) or \( \frac{5x + 5}{x} \).
If we just look at the option that resembles a rational expression of the same structure, none match precisely, but the option "Start Fraction 5 x plus 10 over x squared plus 5 x End Fraction" suggests a discrepancy in the arithmetic, so the correct representation doesn't seem to be listed. The answer should be:
\[
\frac{5(x + 1)}{x} \text{ or } \frac{5x + 5}{x}
\]
However, based on the closest evaluations from your responses, none are accurate. Please double-check any equations or simplifications if needed.
1. Convert \( 5 \) into a fraction:
\[
5 = \frac{5x}{x}
\]
2. Now, we can combine the expressions:
\[
\frac{2}{x} + \frac{3}{x} + \frac{5x}{x} = \frac{2 + 3 + 5x}{x}
\]
\[
= \frac{5x + 5}{x}
\]
3. The expression can also be factored:
\[
= \frac{5(x + 1)}{x}
\]
Thus, the final result, in terms of a single rational expression, is \( \frac{5(x + 1)}{x} \).
From the options provided, none of them correctly represent the simplified sum \( \frac{5(x + 1)}{x} \) or \( \frac{5x + 5}{x} \).
If we just look at the option that resembles a rational expression of the same structure, none match precisely, but the option "Start Fraction 5 x plus 10 over x squared plus 5 x End Fraction" suggests a discrepancy in the arithmetic, so the correct representation doesn't seem to be listed. The answer should be:
\[
\frac{5(x + 1)}{x} \text{ or } \frac{5x + 5}{x}
\]
However, based on the closest evaluations from your responses, none are accurate. Please double-check any equations or simplifications if needed.