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√
Answers
GPT-4o mini
A rational expression is defined as the quotient of two polynomials. Let's analyze the options provided:
1. \( \frac{x^{\frac{3}{2}} + 5}{2x^{9}} \) - This is a rational expression because both the numerator and denominator are polynomials.
2. \( \frac{8x^{2} + 7}{0} \) - This is not a valid rational expression because the denominator cannot be zero.
3. \( \frac{5.3}{2x - 1} \) - This can be rewritten as \( \frac{5.3}{2x - 1} \), which is valid since \( 5.3 \) is a constant (considered a polynomial of degree 0) and \( 2x - 1 \) is a polynomial.
4. \( 9x - 48 + x\sqrt{} \) - This is incomplete because it appears to have \( x\sqrt{} \) which is not defined without a specific value or operation inside the square root, making it not a rational expression.
So, the choices that are rational expressions are:
- \( \frac{x^{\frac{3}{2}} + 5}{2x^{9}} \)
- \( \frac{5.3}{2x - 1} \)
Gina could choose either of the first or third options as they represent valid rational expressions.
1. \( \frac{x^{\frac{3}{2}} + 5}{2x^{9}} \) - This is a rational expression because both the numerator and denominator are polynomials.
2. \( \frac{8x^{2} + 7}{0} \) - This is not a valid rational expression because the denominator cannot be zero.
3. \( \frac{5.3}{2x - 1} \) - This can be rewritten as \( \frac{5.3}{2x - 1} \), which is valid since \( 5.3 \) is a constant (considered a polynomial of degree 0) and \( 2x - 1 \) is a polynomial.
4. \( 9x - 48 + x\sqrt{} \) - This is incomplete because it appears to have \( x\sqrt{} \) which is not defined without a specific value or operation inside the square root, making it not a rational expression.
So, the choices that are rational expressions are:
- \( \frac{x^{\frac{3}{2}} + 5}{2x^{9}} \)
- \( \frac{5.3}{2x - 1} \)
Gina could choose either of the first or third options as they represent valid rational expressions.