Punctul a)
[tex] E(x) =\left(\dfrac{1}{x+2} -\dfrac{1}{2x+1}\right) :\dfrac{1}{2x^2+5x+2} \\ E(x)=\dfrac{2x+1-(x+2)}{(x+2)(2x+1)} :\dfrac{1}{2x^2 +x+4x+2} \\ E(x) = \dfrac{2x+1-x-2}{(x+2)(2x+1)} :\dfrac{1}{x(2x+1)+2(2x+1)} \\ E(x) = \dfrac{x-1}{(x+2)(2x+1)} \cdot (x+2)(2x+1) \\ \tt E(x) = x-1 \ , \ \forall x\in \mathbb{R} - \{-2,-\tfrac{1}{2}\} [/tex]
Punctul b)
[tex] E(-x) \cdot E(x) \leq 1 \\ (-x-1)(x-1) \leq 1 \\ -(x+1)(x-1) \leq 1 \\ -(x^2 -1) \leq 1 \\ x^2-1 \geq -1 \\ x^2 \geq 0 \implies adevarat \\ \iff \tt E(-x) \cdot E(x) \leq 1 \ , \ \forall x\in \mathbb{R} -\{-2,-\tfrac{1}{2}\} [/tex]
