ÖMO 1990 Problem 4

For each nonzero integer $n$ find all functions $f: \mathbb{R} - \{-3,0 \} \rightarrow \mathbb{R}$ satisfying:

$f(x+3)+f \left( -\frac{9}{x} \right)=\frac{(1-n)(x^2+3x-9)}{9n(x+3)}+\frac{2}{n}$ for all $x \not= 0,-3.$

Furthermore, for each fixed $n$ find all integers $x$ for which $f(x)$ is an integer.