a)
[tex]\frac{x(x-5)(x+\frac{1}{3})}{(3x+1)(x+2)}=0\\\\(3x+1)(x+2)\neq0\\\\x\neq-\frac{1}{3}, \ x\neq-2\\\\x(x-5)(x+\frac{1}{3})=0\\\\x=0 \ \vee \ x-5=0 \ \vee \ x+\frac{1}{3}=0\\\\\boxed{x=0}\in\mathbb{D} \ \vee \ \boxed{x=5}\in\mathbb{D} \ \vee \ x=-\frac{1}{3}\notin\mathbb{D}[/tex]
Odp. x = 0 lub x = 5.
b)
[tex]\frac{x(x+2)(x-4)}{x(x-2)(x+4)}=0\\\\x(x-2)(x+4)\neq0\\\\x\neq0, \ x\neq2, \ x\neq-4\\\\x(x+2)(x-4)=0\\\\x=0 \ \vee \ x+2=0 \ \vee \ x-4=0\\\\x=0\notin\mathbb{D} \ \vee \ \boxed{x=-2}\in\mathbb{D} \ \vee \ \boxed{x=4}\in\mathbb{D}[/tex]
Odp. x = -2 lub x = 4.
c)
[tex]\frac{x^2(x-3)(x+2)}{x(x+2)(4-x)}=0\\\\x^2(x-3)(x+2)\neq0\\\\x\neq0, \ x\neq3, \ x\neq-2\\\\x(x+2)(4-x)=0\\\\x=0 \ \vee \ x+2=0 \ \vee \ 4-x=0\\\\x=0\notin\mathbb{D} \ \vee \ x=-2\not\in\mathbb{D} \ \vee \ \boxed{x=4}\in\mathbb{D}[/tex]
Odp. x = 4.
