[tex]a)\\\frac{x^{2}+6x}{x^{2}-6x} = 0 \ \ /\cdot(x^{2}-6x)\\\\x^{2}-6x \neq 0\\x(x - 6) \neq 0\\D = R\setminus\{0,6\}\\\\x^{2}+6x = 0\\\\x(x+6) = 0\\\\x = 0 \ \ \not\in D \ \ \vee \ \ x = -6\\\\x = -6[/tex]
[tex]b)\\\frac{x-2}{x+3} = 1 \ \ /\cdot(x+3)\\\\x+3 \neq 0\\x \neq -3\\D = R \setminus\{-3\}\\\\x-2 = x+3\\\\x-x = 3+2\\\\0 = 5, \ szprzecznosc, \ brak \ rozww\\\\0 \neq 5[/tex]
[tex]c)\\\frac{x-1}{x-2} = 3 \ \ /\cdot(x-2)\\\\x-2 \neq 0\\x \neq 2\\D = R \setminus\{2\}\\\\x-1 = 3(x-2)\\\\x-1 = 3x-6\\\\x-3x = -6+1\\\\-2x = -5 \ \ /:(-2)\\\\x = 2,5[/tex]
[tex]d)\\\frac{x+3}{x+1} = 4 \ \ /\cdot(x+1)\\\\x+1 \neq 0\\x \neq -1\\D = R \setminus\{-1\}\\\\x+3 = 4(x+1)\\\\x+3 = 4x+4\\\\x - 4x = 4-3\\\\-3x = 1 \ \ /:(-3)\\\\x = -\frac{1}{3}[/tex]
[tex]e)\\\frac{x}{x+2} = 6 \ \ /\cdot(x+2)\\\\x+2 \neq 0\\x \neq -2\\D = R\setminus\{-2\}\\\\x = 6(x+2)\\\\x = 6x + 12\\\\x - 6x = 12\\\\-5x = 12 \ \ /:(-5)\\\\x = -2,4[/tex]
