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 5.32x−1 Start Fraction 5.3 over 2 x minus 1 End Fraction 9x−48+x√ Start Fraction 9 x minus 4 over 8 plus Start Root x End Root End Fraction 8x2+70
Answers
GPT-4o mini
A rational expression is defined as a fraction where the numerator and the denominator are both polynomials.
Let's analyze the given options to identify which one is a rational expression:
1. **\(x^{32} + 52x^9\)**: This is a polynomial and is not a fraction, so it is not a rational expression.
2. **\(\frac{x^{\frac{3}{2}} + 5}{2x^{9}}\)**: Here, the numerator \(x^{\frac{3}{2}} + 5\) contains \(x^{\frac{3}{2}}\), which is not a polynomial term due to the fractional exponent. Thus, this is not a rational expression.
3. **\(\frac{5.3}{2x - 1}\)**: This is a fraction where both the numerator \(5.3\) (a constant) and the denominator \(2x - 1\) (a polynomial) are valid. Hence, this is a rational expression.
4. **\(\frac{9x - 4}{8 + \sqrt{x}}\)**: The denominator \(8 + \sqrt{x}\) contains \(\sqrt{x}\), which is not a polynomial term. Therefore, this is not a rational expression.
5. **\(8x^2 + 70\)**: Similar to the first option, this is a polynomial and not a fraction, so it is not a rational expression.
From this analysis, the only option that is a rational expression is:
**\(\frac{5.3}{2x - 1}\)**.
Let's analyze the given options to identify which one is a rational expression:
1. **\(x^{32} + 52x^9\)**: This is a polynomial and is not a fraction, so it is not a rational expression.
2. **\(\frac{x^{\frac{3}{2}} + 5}{2x^{9}}\)**: Here, the numerator \(x^{\frac{3}{2}} + 5\) contains \(x^{\frac{3}{2}}\), which is not a polynomial term due to the fractional exponent. Thus, this is not a rational expression.
3. **\(\frac{5.3}{2x - 1}\)**: This is a fraction where both the numerator \(5.3\) (a constant) and the denominator \(2x - 1\) (a polynomial) are valid. Hence, this is a rational expression.
4. **\(\frac{9x - 4}{8 + \sqrt{x}}\)**: The denominator \(8 + \sqrt{x}\) contains \(\sqrt{x}\), which is not a polynomial term. Therefore, this is not a rational expression.
5. **\(8x^2 + 70\)**: Similar to the first option, this is a polynomial and not a fraction, so it is not a rational expression.
From this analysis, the only option that is a rational expression is:
**\(\frac{5.3}{2x - 1}\)**.