Odpowiedź:
[tex]a)\\\\\frac{3x-4}{2}=\frac{4x-5}{3}\\\\3(3x-4)=2(4x-5)\\\\9x-12=8x-10\\\\9x-8x=-10+12\\\\x=2\\\\\\b)\ \ \frac{x}{2}=\frac{8}{x}\ \ \ \ x\neq 0\\\\x^2=16\\\\x^2-16=0\\\\(x-4)(x+4)=0\\\\x-4=0\ \ \ \ \vee\ \ \ \ x+4=0\\\\x=4\ \ \ \ \ \ \ \ \ \ \vee\ \ \ \ x=-4[/tex]
[tex]c)\\\\\frac{2}{x^2}=\frac{1}{3}\\\\x^2\neq 0\\x\neq 0\\\\6=x^2\\\\x^2=6\\\\x^2-6=0\\\\(x-\sqrt{6})(x+\sqrt{6})=0\\\\x-\sqrt{6}=0\ \ \ \ \vee\ \ \ \ x+\sqrt{6}=0\\\\x=\sqrt{6}\ \ \ \ \ \ \ \ \vee\ \ \ \ x=-\sqrt{6}\\\\\\d)\\\\\frac{1}{x-1}+2=0\\\\x-1\neq 0\\x\neq 1\\\\\frac{1}{x-1}=-2\ \ /\cdot(x-1)\\\\1=-2(x-1)\\\\1=-2x+2\\\\2x=2-1\\\\2x=1\ \ /:2\\\\x=\frac{1}{2}[/tex]
[tex]e)\\\\\frac{3(x-1)}{5}-\frac{x-3}{2}=\frac{x-8}{10}\\\\\frac{3x-3}{5}-\frac{x-3}{2}=\frac{x-8}{10}\ \ /\cdot10\\\\2(3x-3)-5(x-3)=x-8\\\\6x-6-5x+15=x-8\\\\x+9=x-8\\\\x-x=-8-9\\\\0=-17\\\\R\'ownanie\ \ sprzeczne\ \ nie\ \ ma\ \ rozwiazania[/tex]
[tex]f)\\\\\frac{3(x-11)}{4}=\frac{3(x+1)}{5}-\frac{2(2x-5)}{11}\\\\\frac{3x-33}{4}=\frac{3x+3}{5}-\frac{4x-10}{11}\ \ /\cdot220\\\\55(3x-33)=44(3x+3)-20(4x-10)\\\\165x-1815=132x+132-80x+200\\\\165x-1815=52x+332\\\\165x-52x=332+1815\\\\113x=2147\ \ /:113\\\\x=19[/tex]
[tex]g)\\\\\frac{x(x-1)}{4}-\frac{2x^2+1}{2}=-\frac{3}{4}x^2-0,25(x+2)\\\\\frac{x^2-x}{4}-\frac{2x^2+1}{2}=-\frac{3}{4}x^2-0,25x-0,5\ \ /\cdot4\\\\x^2-x-2(2x^2+1)=-3x^2-x-2\\\\x^2-x-4x^2-2=-3x^2-x-2\\\\-3x^2-x+3x^2+x=-2+2\\\\0=0\\\\R\;ownanie\ \ to\.zsamo\'sciowe\ \ ma\ \ niesko\'nczenie\ \ wiele\ \ rozwiaza\'n[/tex]
[tex]h)\\\\\dfrac{x+\frac{4-x}{3}}{5}=\dfrac{x-\frac{x-5}{5}}{3}\\\\3(x+\frac{4-x}{3})=5(x-\frac{x-5}{5})\\\\3x+\not3\cdot\frac{4-x}{\not3}=5x-\not5\cdot\frac{x-5}{\not5}\\\\3x+(4-x)=5x-(x-5)\\\\3x+4-x=5x-x+5\\\\2x+4=4x+5\\\\2x-4x=5-4\\\\-2x=1\ \ /:(-2)\\\\x=-\frac{1}{2}[/tex]
