Finding $f(x)$ from the functional equation $f(x)=x f\left(\frac{2x+3}{x-2}\right)+3$

Question

Find $f(x)$ if $$f(x)=\begin{cases} x\cdot f\left(\frac{2x+3}{x-2}\right)+3 \ , &\text{if } x\ne 2\\ 0 \ , &\text{if }x=2 \end{cases} $$

No idea how to begin. I just noticed that $f(0)=3.$

Answer 1

Prove that $$f(y)=yf(x)+3,$$where $y=\frac{2x+3}{x-2}$ and solve the system