Răspuns:
[tex]\boldsymbol {\red{E(x)=2}}[/tex]
Explicație pas cu pas:
[tex]E(x) = \bigg (\dfrac{x-1-(x+1)}{x-1} + \dfrac{4(x+1)}{(x-1)(x+1)}\bigg)(x + 1) - \dfrac{4}{x-1} \\ [/tex]
[tex]E(x) = \bigg (\dfrac{-2}{x-1} + \dfrac{4}{x-1}\bigg)(x + 1) - \dfrac{4}{x-1} \\ [/tex]
[tex]E(x) = \dfrac{2(x + 1)}{x-1} - \dfrac{4}{x-1} \\ [/tex]
[tex]E(x) = \dfrac{2x + 2 - 4}{x-1} = \dfrac{2(x - 1)}{x-1}[/tex]
[tex] \implies \bf E(x) = 2[/tex]
q.e.d.
