[tex]\frac{4x^{2}}{x-3}\vdots 4\Rightarrow \frac{4x^{2}}{4(x-3)}\in Z\Rightarrow \frac{x^{2}}{x-3}\in Z\\\frac{x^{2}}{x-3}=\frac{x^{2}-6x+9+6x-18+9}{x-3}\\=\frac{(x-3)^{2}+6(x-3)+9}{x-3}=x-3+6+\frac{9}{x-3}=x+3+\frac{9}{x-3}\\\frac{x^{2}}{x-3}\in Z\Rightarrow \frac{9}{x-3}\in Z\\\Rightarrow 9\vdots (x-3)\Rightarrow (x-3)\in U(9)=\left \{ \pm1;\pm3\pm9 \right \}\\\Rightarrow x\in \left \{ ... \right \}[/tex]