Răspuns:
Explicație pas cu pas:
[tex]E(x)=(\frac{x}{x^{2} -1} -\frac{6}{x^{2} +2x+1} )\cdot (1+\frac{1}{x-2} )\\\\E(x)=(\frac{x}{(x-1)(x+1)} -\frac{6}{(x+1)^2} )\cdot (\frac{x-2+1}{x-2} )\\\\[/tex]
Aducem la acelasi numitor in paranteza adica (x-1)(x+1)²
Pe prima amplificam cu x+1 si pe a doua cu x-1
[tex]E(x)=\frac{x^{2} +x-6x+6}{(x-1)(x+1)^2} )\cdot \frac{x-1}{x-2} \\\\E(x)=\frac{x^{2} -5x+6}{(x-1)(x+1)^2} )\cdot \frac{x-1}{x-2}[/tex]
se simplfifica x-1
[tex]E(x)=\frac{x^{2} -5x+6}{(x+1)^2} \cdot \frac{1}{x-2}\\\\E(x)=\frac{(x-2)(x-3)}{(x+1)^2} \cdot \frac{1}{x-2}\\\\E(x)=\frac{(x-3)}{(x+1)^2}[/tex]
E(x)≤0
avand in vedere ca numitorul (x+1)²>0⇒ x-3≤0
x≤3
x∈(-∞,+3]
