Răspuns :
[tex]E(x)=\dfrac{(x+1)^2-4}{x}:\dfrac{x^2-x}{x^2} \\ E(x)=\dfrac{(x+1)^2-4}{x}\cdot\dfrac{x^2}{x^2-x} \\ E(x)=\dfrac{[(x+1)^2-4]x}{x^2-x} \\ E(x)=\dfrac{(x+1)^2-4}{x-1} \\ E(x)=\dfrac{[(x+1)-2][(x+1)+2]}{x-1} \\ E(x)=\dfrac{(x-1)(x+3)}{x-1} \\ E(x)=x+3.[/tex]
(x+1)² -4 x²-x (x+1-2)( x+1+2) x² (x-1)( x+3) x²
--------------- : ------- = ------------------------ * -------------- = ---------------- * --------- =
x x² x x(x-1) x x(x-1
x*(x-1)( x+3)
----------------- = x+3
x(x-1 )
x x² x x(x-1) x x(x-1
x*(x-1)( x+3)
----------------- = x+3
x(x-1 )