Inversezi mai intai prima fractie, pentru ca este ridicata la puterea -1:
[tex](\frac{x+2}{2})^{-1}=\frac{2}{x+2}[/tex]
Aduci la acelasi numitor in paranteza de langa (x+2):
[tex]1-\frac{2x}{(x+2)^2}=\frac{(x+2)^2-2x}{(x+2)^2}=\frac{x^2+4x+4-2x}{(x+2)^2} =\frac{x^2+2x+4}{(x+2)^2}[/tex]
Aduci la acelasi numitor si in ultima paranteza:
[tex]x+2+\frac{4}{x}=\frac{x^2+2x+4}{x}[/tex]
Faci calculul:
[tex]E(x)=\frac{2}{x+2}+(x+2)*\frac{x^2+2x+4}{(x+2)^2}:\frac{x^2+2x+4}{x} \\ E(x)=\frac{2}{x+2}+\frac{x^2+2x+4}{x+2}*\frac{x}{x^2+2x+4} \\ E(x) = \frac{2}{x+2}+\frac{x}{x+2}=\frac{x+2}{x+2}=\ \textgreater \ E(x)=1, x \in \mathbb{R} - \{-2,0}\}[/tex]
