Question

E(x)=(1/x-2 - 2/x + 1/x+2) : 4/x(x^2-4). Arătați că E(x)=2

Answer 1

[tex]E(x)=\left(\dfrac{1}{x-2}-\dfrac{2}{x}+\dfrac{1}{x+2}\right ):\dfrac{4}{x(x^2-4)}\\ E(x)= \dfrac{x(x+2)-2(x-2)(x+2)+x(x-2)}{(x-2)x(x+2)}\cdot \dfrac{x(x-2)(x+2)}{4}\\ E(x)=\dfrac{x^2+2x-2x^2+8+x^2-2x}{4}\\ E(x)=\dfrac{8}{4}=2\forall x\in \mathbb{R}\backslash\{\pm 2,0\}[/tex]