Question

Gina is asked to identify a rational expression. Which of the following could she choose?(1 point)
Responses

x^3/2+5/2x^9
Start Fraction x superscript Start Fraction 3 over 2 End Fraction baseline plus 5 over 2 x superscript 9 baseline End Fraction

5.3/2x−1
Start Fraction 5.3 over 2 x minus 1 End Fraction

8x^2+7/0
Start Fraction 8 x squared plus 7 over 0 End Fraction

9x−4/8+√x
Start Fraction 9 x minus 4 over 8 plus Start Root x End Root End Fraction

Answer 1

A rational expression is defined as the quotient of two polynomials. Let's analyze the options:

1. **\( \frac{x^{3/2} + 5}{2x^{9}} \)**: The term \( x^{3/2} \) is not a polynomial because it has a fractional exponent. Thus, this is not a rational expression.

2. **\( \frac{5.3}{2x - 1} \)**: Both the numerator (5.3, which is a constant) and the denominator (2x - 1, which is a polynomial) are polynomials. Therefore, this is a rational expression.

3. **\( \frac{8x^2 + 7}{0} \)**: The denominator is 0, which is undefined. Thus, this is not a rational expression.

4. **\( \frac{9x - 4}{8 + \sqrt{x}} \)**: The term \( \sqrt{x} \) is not a polynomial (it's a root), so this is not a rational expression.

The only valid option that Gina could choose as a rational expression is:

**\( \frac{5.3}{2x - 1} \)**.