The hyperreals don't fix the x/0 or 0/0 problems. Infinitesimals have a well-defined division and take the place of a lot of uses of 0 in the reals, but the hyperreals still have a 0, and the same problem posed in their comment exists when you consider division on the hyperreals as well.
I'm also curious what they intended, but there aren't many options:
1. The question is ill-posed. The input types are too broad.
2. You must extend ℝ with at least one additional point representing the result. Every choice is bad for a number of reasons (e.g., you no longer have multiplicative inverses and might not even have well-defined addition or subtraction on the resulting set). Some are easier to work with than others. A dedicated `undefined` value is usually easy enough to work with, though sometimes a single "infinity" isn't terrible (if you consider negative infinities it gets more terrible).
3. You arbitrarily choose some real-valued result. Basically every theorem or application considering division now doesn't have to special-case zero (because x/0 is defined) but still has to special-case zero (because every choice is wrong for most use cases), leading to no real improvements.
I'm also curious what they intended, but there aren't many options:
1. The question is ill-posed. The input types are too broad.
2. You must extend ℝ with at least one additional point representing the result. Every choice is bad for a number of reasons (e.g., you no longer have multiplicative inverses and might not even have well-defined addition or subtraction on the resulting set). Some are easier to work with than others. A dedicated `undefined` value is usually easy enough to work with, though sometimes a single "infinity" isn't terrible (if you consider negative infinities it gets more terrible).
3. You arbitrarily choose some real-valued result. Basically every theorem or application considering division now doesn't have to special-case zero (because x/0 is defined) but still has to special-case zero (because every choice is wrong for most use cases), leading to no real improvements.