Functional Equation by Substitution?

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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 $

I suppose I can 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 was hoping someone would be able to give me a hint or two about how best to proceed (not looking for a full solution).

Thank you.