Question

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

x32+52x9
Start Fraction x superscript Start Fraction 3 over 2 End Fraction baseline plus 5 over 2 x superscript 9 baseline End Fraction

8x2+70
Start Fraction 8 x squared plus 7 over 0 End Fraction

5.32x−1
Start Fraction 5.3 over 2 x minus 1 End Fraction

9x−48+x√

Answer 1

To identify a rational expression, we need to look for an expression that can be written as the ratio of two polynomials. Let's examine each of the options:

1. **\( \frac{x^{\frac{3}{2}} + \frac{5}{2} x^{9}}{} \)**
This is not a rational expression because the exponent \(\frac{3}{2}\) makes \(x^{\frac{3}{2}}\) not a polynomial (since rational expressions require integer exponents).

2. **\( \frac{8x^{2} + 7}{0} \)**
This cannot be considered a rational expression because the denominator is zero, which would make the expression undefined.

3. **\( 5.3 \div (2x - 1) \)**
This can be rewritten as a rational expression: \( \frac{5.3}{2x - 1} \). It is a ratio of a polynomial (\(2x - 1\)) and a constant (\(5.3\)), which qualifies it as a rational expression.

4. **\( 9x - 48 + x\sqrt{} \)**
The term \(x\sqrt{}\) appears to be incomplete and does not represent a polynomial term. Therefore, it is not a rational expression.

From these analyses, the choice that Gina could make as a rational expression is:

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