Overloading Arithmetic Assignment Operators

[Zampano]

The book I'm using told me to overload these operators like this (example using a fractions class):

code:

rational& operator += (const rational& x) {         den *= x.den;         num = num * x.den + den * x.num;         reduce ();         return *this; }

with the function being declared as public. However, g++ gave an error asking that arithmetic assignment operators always have two parameters. So, I made the function declaration:

code:

friend rational& operator += (rational&, const rational&);

and the implementation to:

code:

rational& operator += (rational& x, const rational& y) {         x.den *= y.den;         x.num = x.num * y.den + y.num * x.den;         x.reduce ();         return *this; }

because at that point I had lost myself and wasn't sure if a number of things were valid, such as *this with no owner object. No the compiler gives errors because it can't read the num and den, the two private variables, even though the function is a friend.
I attach the rest of the code, declaration, implementation, and driver (testing the assignment operator) in one file.
Help, please?

[OneOffDriveByPoster]

You should return x instead of *this. You still had the x as a const reference in the attached file--fix it.

[Zampano]

*gulps* Uh, thanks.
I'm a bit embarrassed that it was such a little problem.

[wtd]

Be embarassed, but be glad.