To identify a rational expression, we need to look for an expression that can be written as the ratio of two polynomials. Let's examine each of the options:
-
\( \frac{x^{\frac{3}{2}} + \frac{5}{2} x^{9}}{} \)
This is not a rational expression because the exponent \(\frac{3}{2}\) makes \(x^{\frac{3}{2}}\) not a polynomial (since rational expressions require integer exponents). -
\( \frac{8x^{2} + 7}{0} \)
This cannot be considered a rational expression because the denominator is zero, which would make the expression undefined. -
\( 5.3 \div (2x - 1) \)
This can be rewritten as a rational expression: \( \frac{5.3}{2x - 1} \). It is a ratio of a polynomial (\(2x - 1\)) and a constant (\(5.3\)), which qualifies it as a rational expression. -
\( 9x - 48 + x\sqrt{} \)
The term \(x\sqrt{}\) appears to be incomplete and does not represent a polynomial term. Therefore, it is not a rational expression.
From these analyses, the choice that Gina could make as a rational expression is:
\( \frac{5.3}{2x - 1} \)