calculation $f(x)$ from given expression $$f(x)+xf(-x)=x-2$$
what is $f(x$)?
I try to solve this problem, but I don't know how to remove $f(-x)$ or converting it to $f(x)$.

After solving such task as in the above answers, you should always test it: you put $\frac{x^2 +3x - 2}{1+x^2}$ instead of $f(x)$ into the given equation:
$$\frac{x^2 +3x - 2}{1+x^2} + x\frac{x^2 -3x - 2}{1+x^2} =$$
$$= \frac{x^2 + 3x - 2 +x^3 - 3x^2 - 2x}{1+x^2} =$$
$$= \frac{x^3 - 2x^2 + x - 2}{1+x^2} =$$
$$= \frac{(x-2) (x^2+1)}{1+x^2} = x-2$$
I forgot to do it once on a maths competition and it cost me a point.
