[tex]f(x) =\frac{2x^{2}+4x-6}{x^{3}-2x^{2}-5x+6}\\\\\\Dziedzina\\\\x^{3}-2x^{2}-5x+6 \neq 0\\\\x^{3}-x^{2}-x^{2}+x-6x+6 \neq 0\\\\x^{2}(x-1)-x(x-1)-6(x-1) \neq 0\\\\(x-1)(x^{2}-x-6) \neq 0\\\\(x-1)(x^2 - 3x + 2x - 6)\neq 0\\\\(x-1)[x(x-3)+2(x-3)]\neq 0\\\\(x-1)(x-3)(x+2)\neq 0\\\\x \neq 1 \ \ i \ \ x \neq 3 \ \ i \ \ x \neq -2\\\\\boxed{D = R \setminus\{-2, 1,3\}}[/tex]
[tex]2x^{2}+4x-6 = 0 \ \ /:2\\\\\underline{x^{2}+2x-3 = 0}\\\\\Delta = 2^{2}-4\cdot(-3) = 4+12 = 16\\\\\sqrt{\Delta} = \sqrt{16} = 4\\\\x_1 = \frac{-b-\sqrt{\Delta}}{2a} = \frac{-2-4}{2} = \frac{-6}{2} = -3\\\\x_2 = \frac{-b+\sqrt{\Delta}}{2a} = \frac{-2+4}{2} =\frac{2}{2} = 1 \ \notin D\\\\\boxed{x = -3}[/tex]
