[tex]zad.1\\\\zal.~~3x-2\neq 0~~\Rightarrow ~~x\neq \dfrac{2}{3}~~\Rightarrow ~~D= R-\{\dfrac{2}{3} \} \\\\\dfrac{6x-1}{3x-2} =3x+2\\\\\\\dfrac{6x-1}{3x-2} =\dfrac{3x+2}{1} \\\\(3x-2)\cdot (3x+2)=6x-1\\\\(3x)^{2} -2^{2} =6x-1\\\\9x^{2} -4-6x+1=0\\\\9x^{2} -6x-3=0~~\mid \div 3\\\\3x^{2} -2x-1=0\\\\\Delta=(-2)^{2} -4\cdot 3\cdot (-1)=4+12=16\\\\\sqrt{\Delta} =4\\\\x_{1} =\dfrac{2-4}{6} ~~\lor~~x_{2} =\dfrac{2+4}{6} \\\\(~~x_{1} =-\dfrac{1}{3} ~~\lor ~~x_{2} =1~~)~~\land ~~x\in D~~[/tex]
[tex]x=-\dfrac{1}{3} ~~\lor~~x=1\\\\\\Odp:~~x=-\dfrac{1}{3} ~~\lor~~x=1[/tex]
[tex]zad.2\\\\(2x-1)\cdot (x^{2} -x-6)=0\\\\x^{2} -x-6=0 ~~\lor ~~2x-1=0\\\\x^{2} -x-6=0 ~~\lor~~ x=\dfrac{1}{2} \\\\\Delta=(-1)^{2} -4\cdot1\cdot (-6)\\\\\Delta=1+24\\\\\Delta=25\\\\\sqrt{\Delta}=5\\\\x_{1} =\dfrac{1-5}{2}=-2 \\\lor\\x_{2} =\dfrac{1+5}{2}=3\\\\\\x=-2~~\lor~~x=3~~\lor~~x=\dfrac{1}{2} \\\\\\Odp:~~x=-2~~\lor~~x=3~~\lor~~x=\dfrac{1}{2}[/tex]
