Finding function $f(x)$ which satisfy given functional equation 
Find all function $f:\mathbb{R}-\{0,1\}$ in $$f(x)+2f\left(\frac{1}{x}\right)+3f\left(\frac{x}{x-1}\right)=x$$

Attempt: put $\displaystyle x = \frac{1}{x}$, then $$f\left(\frac{1}{x}\right)+2f(x)+3f\left(\frac{1}{1-x}\right) = \frac{1}{x}$$
could some help me how to solve it , thanks

I do not understand the phrase "A detailed canonical answer is required to address all the concerns" since I am unaware of any concerns about the answer given some time ago. However, here are the actual equations and how to solve them.
Let $V = \pmatrix{f(x)\\f(\frac{1}{x})\\f(\frac{1}{1-x})\\f(\frac{x}{x-1})\\f(\frac{x-1}{x})\\f(1-x)},$      $W = \pmatrix{x\\\frac{1}{x}\\1-x\\\frac{x-1}{x}\\\frac{x}{x-1}\\\frac{1}{1-x}\\}$
Then $$ \pmatrix{1&2&0&3&0&0\\2&1&3&0&0&0\\0&0&2&0&3&1\\0&0&0&2&1&3\\3&0&0&1&2&0\\0&3&1&0&0&2}V=W$$
Multiplying on the left by $ \pmatrix{-3&3&-5&1&7&1}$ gives $$24f(x)=\pmatrix{-3&3&-5&1&7&1}W$$
Thus giving the answer noted above.
