Rozwiązanie równania :
[tex]\frac{x+2}{x^2-2}=x\\\\x^2-2\neq0\\\\(x+\sqrt2)(x-\sqrt2)\neq0\\\\x\neq-\sqrt2, \ x\neq\sqrt2\\\\\mathbb{D}:\mathbb{R} \ -\{-\sqrt2,\sqrt2\}\\\\x(x^2-2)=x+2\\\\x^3-2x-x-2=0\\\\x^3-3x-2=0\\\\x(x^2-4)+x-2=0\\\\x(x+2)(x-2)+x-2=0\\\\(x-2)(x(x+2)+1)=0\\\\(x-2)(x^2+2x+1)=0\\\\(x-2)(x+1)^2=0\\\\x-2=0 \ \vee \ x+1=0\\\\x=2\in\mathbb{D} \ \vee \ x=-1\in\mathbb{D}[/tex]
