Answer: Choice A) z
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Explanation:
x and y are two integers, with x being nonzero
This means x/y is rational as long as y is nonzero as well. If y = 0, then we have a division by zero error. Try something like 1/0 on your calculator and you'll find it doesn't work.
Similarly, y/x is rational as well. Any rational number is simply dividing two integers as a fraction like this. Other examples include stuff like 1/2, 4/5, 8/17, and so on.
Since y is an integer, this means we can write it like this: y = y/1. This shows any integer is also rational, but not the other way around. A fraction like 2/3 is rational but not an integer.
All of what was discussed above indicates that choices B, C and D can be ruled out. The only thing left is choice A. The variable z isn't defined, so it's not clear what it is exactly. But it's likely the answer as it's the only thing left after the eliminations.
