I've been trying to solve this:
$f: \Bbb{R\setminus \{1\} \to \Bbb{R}}, f(2-x) + x f(\frac{1}{1-x}) = 3-x $
Seems sensible to simplify slightly by replacing $x$ with $(2-x)$ to give:
$f(x) + (2-x)f(\frac{1}{x-1}) = x+1$
I'm assuming I need to use substitution(s) from here, but I'm embarrassingly rusty at maths these days, and I haven't been able to crack this one. I'm hoping someone will be able to come up with a quick solution and put me out of my misery...
Thank you.