A rational expression is defined as the quotient of two polynomials. Let's analyze each option:
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\( \frac{x^{\frac{3}{2}} + 5}{2x^9} \) - The numerator \(x^{\frac{3}{2}} + 5\) is not a polynomial because it contains a non-integer exponent (\(\frac{3}{2}\)).
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\( \frac{9x - 4}{8 + \sqrt{x}} \) - The denominator \(8 + \sqrt{x}\) contains a square root, which means it is not a polynomial.
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\( \frac{8x^2 + 7}{0} \) - This expression is undefined because division by zero is not allowed. While the numerator is a polynomial, the expression as a whole is not valid.
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\( \frac{5.3}{2x - 1} \) - This is a valid rational expression. The numerator \(5.3\) can be treated as a polynomial (specifically a constant polynomial), and the denominator \(2x - 1\) is a polynomial as well.
Based on this analysis, Gina could choose the fourth option:
\( \frac{5.3}{2x - 1} \).