To identify a rational expression, we need to find an expression that can be written as a ratio of two polynomials. Here's an analysis of each option provided:
-
\( 8x^2 + 70 \)
- This is a polynomial, but it is not in the form of a rational expression (which needs to be a fraction). So, not a rational expression.
-
\( \frac{8x^2 + 7}{0} \)
- This is undefined because division by zero is not allowed. Therefore, it is not a valid rational expression.
-
\( \frac{x^{\frac{3}{2}} + \frac{5}{2}x^9}{1} \)
- This is a rational expression since it is in the form of a fraction where both the numerator and denominator are polynomials (the denominator is 1, which is also a polynomial).
-
\( \frac{9x - 4}{8 + \sqrt{x}} \)
- The denominator \(8 + \sqrt{x}\) involves a square root, which means it is not a polynomial. Thus, this is not a rational expression.
Based on this evaluation, the only option that qualifies as a rational expression is:
\( \frac{x^{\frac{3}{2}} + \frac{5}{2}x^9}{1} \).