Which of the following is a rational expression? hoose the best answer for the following questions $$ \begin{array}{llll}\left\lvert\, \frac{x+1}{x^{2}+1} ight. & ext { B. } \sqrt{x}+x+1 & ext { C. } \frac{x}{x}\end{array} $$

Question

Which of the following is a rational expression? hoose the best answer for the following questions $$ \begin{array}{llll}\left\lvert\, \frac{x+1}{x^{2}+1}ight. & 	ext { B. } \sqrt{x}+x+1 & 	ext { C. } \frac{x}{x}\end{array} $$

UpStudy AI · Accepted Answer

To determine which of the given options is a rational expression, we need to understand what a rational expression is. A rational expression is a fraction where both the numerator and the denominator are polynomials.

Let's analyze each option:

1. **Option A: $$ \frac{x+1}{x^{2}+1} $$**
   - The numerator $$ x + 1 $$ is a polynomial of degree 1.
   - The denominator $$ x^2 + 1 $$ is a polynomial of degree 2.
   - Since both the numerator and denominator are polynomials, this is a rational expression.

2. **Option B: $$ \sqrt{x} + x + 1 $$**
   - This expression contains a square root, which is not a polynomial. Therefore, this is not a rational expression.

3. **Option C: $$ \frac{x}{x} $$**
   - The numerator $$ x $$ is a polynomial of degree 1.
   - The denominator $$ x $$ is also a polynomial of degree 1.
   - However, this expression simplifies to 1 (for $$ x 
eq 0 $$), which is a constant and can be considered a rational expression.

Based on this analysis, both Option A and Option C can be considered rational expressions, but Option A is the more straightforward example of a rational expression.

Thus, the best answer is:

**A. $$ \frac{x+1}{x^{2}+1} $$**
Option A, $$ \frac{x+1}{x^{2}+1} $$, is a rational expression.

Which of the following is a rational expression?
hoose the best answer for the following questions

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