def add_three(
    x_num: int, x_den: int, y_num: int, y_den: int, z_num: int, z_den: int
) -> tuple[int, int]:
    top: int = x_num * y_den * z_den + y_num * x_den * z_den + z_num * x_den * y_den
    bottom: int = x_den * y_den * z_den
    hcf: int = gcd(top, bottom)
    top //= hcf
    bottom //= hcf
    return top, bottom