Witaj :)
[tex]\Large \boxed{\frac{(x-1)^2(x+x^2+x^3)}{1-x^2} }[/tex]
[tex]1-x^2\neq 0\\-x^2\neq -1\ \ /\cdot (-1)\\x^2\neq 1 \iff x\neq 1\ \ \ \vee\ \ \ x\neq -1\\\\\boxed{D=\mathbb R \setminus \{-1;1\}}[/tex]
[tex]\frac{(x-1)^2(x+2x^2+x^3)}{1-x^2}=0\iff (x-1)^2(x+2x^2+x^3)=0\\\\(x-1)^2(x+2x^2+x^3)=0\iff (x-1)^2=0 \ \ \vee\ \ x+2x^2+x^3=0\\\\(x-1)^2=0\iff \boxed{x=1\ \notin D}\\\\(x+2x^2+x^3)=0\\\\(x^3+2x^2+x)=0\\\\x(x^2+2x+1)=0\iff \boxed{x=0\in D}\ \ \vee \ \ \ x^2+2x+1=0\\\\\ x^2+2x+1=0\\\\(x+1)^2=0\iff \boxed{x=-1\notin D}\\\\MIEJSCA\ ZEROWE:\\\\\boxed{x\in \{0\}}[/tex]
[tex]\Large \boxed{\frac{(x+2)^2-1}{(3+x)^2} }[/tex]
[tex](3+x)^2\neq 0\iff x\neq -3\\\\\boxed{D=\mathbb R\setminus \{-3\}}[/tex]
[tex]\frac{(x+2)^2-1}{(3+x)^2} =0\iff (x+2)^2-1=0\\\\(x+2)^2-1=0\\x^2+4x+4-1=0\\x^2+4x+3=0\\a=1\\b=4\\c=3\\\\\Delta=b^2-4ac=4^2-4\cdot 1\cdot 3=16-12=4>0\\\sqrt{\Delta}=\sqrt{4}=2\\\\x_1=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-4-2}{2\cdot 1}=\frac{-6}{2}=-3 \notin D\\ \\ x_2=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-4+2}{2\cdot 1}=\frac{-2}{2}=-1 \in D \\\\MIEJSCA\ ZEROWE:\\\\\boxed{x\in \{-1\}}[/tex]
