## Example 2. Solve the equation

$$
f\left(\frac{x+1}{x-2}\right)+2 f\left(\frac{x-2}{x+1}\right)=x
$$
Solution. Let $\frac{x-2}{x+1}=z$, then $x=\frac{z+2}{1-z}, \quad(z \neq 1, z \neq 0)$ and

$$
f\left(\frac{1}{z}\right)+2 f(z)=\frac{z+2}{1-z}
$$

Replacing $z$ with $\frac{1}{z}$, we get:

$$
f(z)+2 f\left(\frac{1}{z}\right)=\frac{1+2 z}{z-1}
$$

From equations (3) and (4), we find $f(z): f(z)=\frac{4 z+5}{3(1-z)}$

and accordingly $f(x)=\frac{4 x+5}{3(1-x)}$.

This is the solution to the given equation.