A rational expression is a fraction in which both the numerator and the denominator are polynomials. Let's analyze each of the options provided:
-
\( \frac{9x - 4}{8 + \sqrt{x}} \): The numerator \( (9x - 4) \) is a polynomial, but the denominator \( (8 + \sqrt{x}) \) is not a polynomial because of the square root. So this is not a rational expression.
-
\( \frac{5.3}{2x - 1} \): The numerator \( (5.3) \) is a constant (which is also a polynomial of degree 0), and the denominator \( (2x - 1) \) is a polynomial. Therefore, this is a rational expression.
-
\( \frac{x^{\frac{3}{2}} + \frac{5}{2} x^9}{1} \): The numerator \( (x^{\frac{3}{2}} + \frac{5}{2} x^9) \) contains \( x^{\frac{3}{2}} \), which is not a polynomial since it has a fractional exponent. So this is not a rational expression.
-
\( 8x^2 + 70 \): This is a polynomial but not a rational expression because it is not in the form of a fraction.
Based on this analysis, the only option that qualifies as a rational expression is:
\( \frac{5.3}{2x - 1} \).