Explicație pas cu pas:
a) x ≠ -1
[tex](x + 1) \in \{-4;-2;-1;1;2;4\}[/tex]
[tex]x + 1 = - 4 \implies x = - 5 \\ [/tex]
[tex]x + 1 = - 2 \implies x = - 3 \\ [/tex]
[tex]x + 1 = - 1 \implies x = - 2 \\ [/tex]
[tex]x + 1 = 1 \implies x = 0 \\ [/tex]
[tex]x + 1 = 2 \implies x = 1 \\ [/tex]
[tex]x + 1 = 4 \implies x = 3 \\ [/tex]
[tex]\implies x \in \{-5;-3;-2;0;1;3\}[/tex]
b) x ≠ -½
[tex](2x + 1) \in \{-7;-1;1;7\}[/tex]
[tex]2x + 1 = - 7 \iff 2x = - 8 \implies x = - 4 \\ [/tex]
[tex]2x + 1 = - 1 \iff 2x = - 2 \implies x = - 1 \\ [/tex]
[tex]2x + 1 = 1 \iff 2x = 0 \implies x = 0 \\ [/tex]
[tex]2x + 1 = 7 \iff 2x = 6 \implies x = 3 \\ [/tex]
[tex]\implies x \in \{-4;-1;0;3\}[/tex]
c) x ≠ -2
[tex]\frac{2x + 1}{x + 2} = \frac{2x + 4 - 3}{x + 2} = \frac{2(x + 2) - 3}{x + 2} =2 - \frac{3}{x + 2} \\ [/tex]
[tex](x + 2) \in \{-3;-1;1;3\}[/tex]
[tex]x + 2 = - 3 \implies x = - 5 \\ [/tex]
[tex]x + 2 = - 1 \implies x = - 3 \\ [/tex]
[tex]x + 2 = 1 \implies x = - 1 \\ [/tex]
[tex]x + 2 = 3 \implies x = 1 \\ [/tex]
[tex]\implies x \in \{-5;-3; - 1;1\}[/tex]
