Final answer:
If x and y are both rational numbers, then x remains rational. This is because rational numbers are closed under the basic arithmetic operations and any fraction with the same non-zero numerator and denominator simplifies to 1.
Step-by-step explanation:
The question addresses a concept in mathematics involving rational numbers. If x and y are both rational numbers, then x is also rational, according to the given assertion. In mathematics, a rational number is a number that can be expressed as a fraction a/b, where a and b are integers and b is not zero. Since rational numbers are closed under addition, subtraction, multiplication, and division (except by 0), the result of any of these operations on rational numbers will always be rational. For instance, dividing the price of good 1 by the price of good 2 will result in a rational number if both prices are rational to begin with, as per the ratio of marginal utilities. Similarly, if an equation has the same quantity in both the numerator and the denominator, the value simplifies to 1, which is itself a rational number.