[tex]\dfrac{(5-x)(2x-1)}{(x-2x^{2} )} =0\\\\zal.\\x-2x^{2} \neq 0\\x(1-2x)\neq 0\\x\neq 0~~\lor~~x\neq \frac{1}{2} ~~\Rightarrow~~D=R- \{ 0,\frac{1}{2} \}\\\\(5-x)\cdot (2x-1)=0\\5-x=0~~\lor ~~2x-1=0\\(~~x=5~~\lor~~x=\frac{1}{2} ~~)~~\land~~x\in D~~\Rightarrow~~x=5\\\\Odp: ~~x=5[/tex]
[tex]\dfrac{x^{3} +8}{x^{2} -4} =0\\\\zal.\\x^{2} -4\neq 0\\(x-2)(x+2)\neq 0\\x-2\neq 0~~\lor~~x+2\neq 0\\x\neq 2~~\lor~~x\neq -2~~\Rightarrow~~D=R-\{ -2,2 \}\\\\x^{3} +8=0\\x^{3} +2^{3} =0\\korzystam~~ze~~wzoru~~skroconego~~mnozenia:~~x^{3} +y^{3} =(x+y)(x^{2} -xy+y^{2} )\\(x+2)\cdot (x^{2} -2x+4)=0\\x^{2} -2x+4=0~~\lor~~x+2=0~~\Rightarrow~~x=-2\\a=1,b=-2,c=4\\\Delta =b^{2} -4ac\\\Delta=4-16\\\Delta=-12 ~~\Rightarrow~~\Delta <0~~\Rightarrow~~brak ~~pierwiastkow\\\\[/tex]
[tex]x=-2~~\land~~x\in D~~\land ~~D=R-\{ -2,2 \}~~\Rightarrow~~x\in \oslash\\\\Odp:~~Brak ~~rozwiazan~~x\in \oslash.[/tex]
[tex]\dfrac{x^{2} +4x+4}{(x+2)^{2} } =0\\\\zal.\\(x+2)^{2} \neq 0\\x+2\neq 0\\x\neq -2~~\Rightarrow~~D=R-\{ -2 \}\\\\x^{2} +4x+4=0\\x^{2} +2\cdot 2\cdot x + 2^{2} =0\\korzystam~~ze~~wzoru~~skroconego~~mnozenia:~~(x+y)^{2} =x^{2} +2\cdot x\cdot y + y^{2} \\(x+2)^{2} =0\\x+2=0\\x=-2~~\land~~x\in D~~\land ~~D=R-\{ -2 \}~~x\in \oslash\\\\Odp:~~Brak ~~rozwiazan~~x\in \oslash.[/tex]
