from .math_rational_rational import rational_from_wide, rational_parts
from .math_rational_types import Rational


def divide_rational(a: Rational, b: Rational) -> Rational:
    """a ÷ b, reduced. Dividing by zero is an error, never an infinity."""
    an, ad = rational_parts(a)
    bn, bd = rational_parts(b)
    if bn == 0:
        raise ValueError("division by zero")
    return rational_from_wide(an * bd, ad * bn)