I was recently posed the problem of expressing (x - 1)/(x + 1) as the sum of an even and odd function. The person who posed the problem suggested that I couldn't solve it.

This is how I went about doing the problem:

First, let's model our problem:

Furthermore, let us write a system of equations:

Now we can attempt to solve for g(x):

Can someone check my solution please? This was a problem that took me a decent amount of time and I would appreciate it. Also, does anyone know where this problem came from? As it was one of the more difficult ones I've encountered, I doubt that the person that posed it developed the problem either.