<s>[INST] $f(x)=?$ if we have $f\left(\frac{x}{x^2+x+1}\right)=\frac{x}{x^2-x+1}$ $f(x)=?$
If we have $$f\left(\frac{x}{x^2+x+1}\right)=\frac{x}{x^2-x+1}$$ to fractions are very similar. I don't have an idea to find $f(x)$. Can someone show me a clue ?
 [/INST] HInt: you can take $$x+\frac 1x  =u $$ and turn all the expression into $u$ ,or do like below 
$$\quad{f(\frac{x}{x^2+x+1})=\frac{x}{x^2-x+1}\\
\frac{x}{x^2+x+1}=u\\\frac{x^2+x+1}{x}=\frac 1u\\x+\frac{1}x +1=\frac 1u \\\to x+\frac{1}x =\frac 1u -1\\
\frac{x}{x^2-x+1}=\dfrac{1}{\dfrac{x^2-x+1}{x}}=\\\dfrac{1}{x+\dfrac{1}{x}-1}=\dfrac{1}{(\frac 1u -1)-1}}$$can you go on  ?
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