i)
[tex]\frac{x+2}{10x-2} = \frac{1}{x+2}\\\\\\Zal: \ \ 10x-2 \neq 0 \ \ \rightarrow \ \ x \neq \frac{1}{5} \ \ i \ \ x \neq -2\\\\\\(x+2)(x+2) = 10x - 2\\\\(x+2)^{2} = 10x-2\\\\x^{2}+4x+4 =10x-2\\\\x^{2}+4x-10x + 4+2 = 0\\\\x^{2}-6x+6 = 0\\\\a = 1, \ b = -6, \ c = 6\\\\\Delta = b^{2}-4ac = (-6)^{2}-4\cdot1\cdot 6 = 36 - 24 = 12\\\\\sqrt{\Delta} = \sqrt{12} = \sqrt{4\cdot3} = 2\sqrt{3}\\\\x_1 = \frac{-b-\sqrt{\Delta}}{2a} = \frac{6-2\sqrt{3}}{2} = 3-\sqrt{3}[/tex]
[tex]x_2 = \frac{-b+\sqrt{\Delta}}{2a} = \frac{6+2\sqrt{3}}{2} = 3+\sqrt{3}\\\\x \in \{3-\sqrt{3}, 3+\sqrt{3}\}[/tex]
j)
[tex]\frac{(x-3)(x-5)(x-6)}{x^{2}-9x+18} = 0\\\\\frac{(x-3)(x-5)(x-6)}{x^{2}-6x-3x+18} = 0\\\\\frac{(x-3)(x-5)(x-6)}{x(x-6)-3(x-6)} =0\\\\\frac{(x-3)(x-5)(x-6)}{(x-6)(x-3)} = 0\\\\\\Zal: \ x \neq 6 \ \ i \ \ x\neq 3\\\\x-5 = 0\\\\\underline{x = 5}[/tex]
