Final answer:
Rational terms can be defined as terms expressed as fractions with polynomials in both the numerator and the denominator. Option B in the given question, 3x²y/2 and 4x³y/3, contains the rational terms as both are in fraction form with polynomial numerators and denominators.
Step-by-step explanation:
The student asked to identify the rational term. A rational term is defined as a term that can be expressed as an exact fraction, where both the numerator and the denominator are polynomials.
In the given options:
- A. xy/2; 6x/y - Here, 'xy/2' is a rational term because it is a fraction with polynomials in the numerator and the denominator. However, '6x/y' is not strictly rational because '6x' and 'y' are not polynomials, although it could be considered rational in a broader sense since it resemble a fraction with one variable in the denominator.
- B. 3x²y/2; 4x³y/3 - Both terms are rational. They have polynomials in both the numerator and the denominator.
- C. ay/x; 3x²y - The first term 'ay/x' is rational, but the second term '3x²y' is not rational since it does not have a denominator term.
- D. 4x²/7; 3a²b/c - The first term '4x²/7' is rational, and the second term '3a²b/c' is also rational, with both terms in the form of a fraction.
The correct answer then must contain only rational terms. Since option B has both of its terms in fraction form with polynomials in the numerator and denominator, option B: 3x²y/2; 4x³y/3 contains the rational terms.