a)
(4x-12)/(x+2)·(2x+4)/(2x-6)=4(x-3)/(x+2) · 2(x+2)/2(x-3)=4 , dla x≠-2 ∧ x≠3
b)
(x²-4)/(x+1):(x+2)/(x²-1)=(x+2)(x-2)/(x+1):(x+2)/(x+1)(x-1)=(x+2)(x-2)/(x+1)·(x+1)(x-1)/(x+2)=(x-1)(x-2) , dla x≠-1 ∧ x≠-2 ∧ x≠1
a)
[tex]x + 2 \neq 0 \implies x \neq -2\\2x - 6 \neq 0 \implies x \neq 3\\D: x \in \mathbb{R} \setminus \{-2,\ 3\}[/tex]
[tex]\frac{4x - 12}{x + 2} \cdot \frac{2x + 4}{2x - 6} =\\\frac{4(x - 3)}{x + 2} \cdot \frac{2(x + 2)}{2(x - 3)} =\\4[/tex]
b)
[tex]x + 1 \neq 0 \implies x \neq -1\\x^2 - 1 \neq 0 \implies x \neq 1 \land x \neq -1\\D: x \in \mathbb{R} \setminus \{-1,\ 1\}[/tex]
[tex]\frac{x^2 - 4}{x + 1} : \frac{x + 2}{x^2 - 1} =\\\frac{(x - 2)(x + 2)}{x + 1} : \frac{x + 2}{(x - 1)(x + 1)} =\\\frac{(x-2)(x+2)(x-1)(x+1)}{(x+1)(x+2)} = \\(x-2)(x-1) =\\x^2 - x - 2x + 2 =\\x^2 - 3x + 2[/tex]