Question
Gina is asked to identify a rational expression. Which of the following could she choose?(1 point) Responses 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 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
Answers
GPT-4o mini
To identify a rational expression, we need to find an expression that can be expressed as the quotient of two polynomials.
Let's analyze each option:
1. **5.32x−1:** This is a polynomial (specifically a linear polynomial) since it does not have a denominator. It is not a rational expression.
2. **Start Fraction 5.3 over 2 x minus 1 End Fraction:** This is a rational expression because it takes the form of a fraction where the numerator is a constant (5.3) and the denominator is a polynomial (2x - 1).
3. **9x−48+x√ Start Fraction 9 x minus 4 over 8 plus Start Root x End Root End Fraction:** This complex expression includes radicals and is not a rational expression. Rational expressions must not have any roots.
4. **x32+52x9 Start Fraction x superscript Start Fraction 3 over 2 End Fraction baseline plus 5 over 2 x superscript 9 baseline End Fraction:** This includes a term with \(x^{\frac{3}{2}}\), which is not a polynomial term since it's not an integer exponent. Therefore, it is not a rational expression.
5. **8x2+70:** This expression is a polynomial (specifically of degree 2). It is not a rational expression because it does not involve any denominators.
From the above options, the only choice that is a rational expression is:
**Start Fraction 5.3 over 2 x minus 1 End Fraction.**
Let's analyze each option:
1. **5.32x−1:** This is a polynomial (specifically a linear polynomial) since it does not have a denominator. It is not a rational expression.
2. **Start Fraction 5.3 over 2 x minus 1 End Fraction:** This is a rational expression because it takes the form of a fraction where the numerator is a constant (5.3) and the denominator is a polynomial (2x - 1).
3. **9x−48+x√ Start Fraction 9 x minus 4 over 8 plus Start Root x End Root End Fraction:** This complex expression includes radicals and is not a rational expression. Rational expressions must not have any roots.
4. **x32+52x9 Start Fraction x superscript Start Fraction 3 over 2 End Fraction baseline plus 5 over 2 x superscript 9 baseline End Fraction:** This includes a term with \(x^{\frac{3}{2}}\), which is not a polynomial term since it's not an integer exponent. Therefore, it is not a rational expression.
5. **8x2+70:** This expression is a polynomial (specifically of degree 2). It is not a rational expression because it does not involve any denominators.
From the above options, the only choice that is a rational expression is:
**Start Fraction 5.3 over 2 x minus 1 End Fraction.**