Expresia din paranteză se poate scrie:
[tex]\it \dfrac{x^3-2x^2}{2x^2}-\dfrac{x^2-4}{4x}=\dfrac{\not x(x^2-2x)}{2x^{\not2}}-\dfrac{x^2-4}{4x}= \dfrac{^{2)}x^2-2x}{2x}-\dfrac{x^2-4}{4x}=\\ \\ \\ =\dfrac{2x^2-4x-x^2+4}{4x}=\dfrac{x^2-4x+4}{4x}=\dfrac{(x-2)^2}{4x}[/tex]
Expresia din enunț devine:
[tex]\it E(x) = \dfrac{(x-2)^2}{4x}\cdot\dfrac{2}{x-2}+\dfrac{1}{2}=\dfrac{x-2}{2x}+\dfrac{^{x)}1}{\ 2}=\dfrac{x-2+x}{2x}=\dfrac{2x-2}{2x}=\\ \\ \\ =\dfrac{2(x-1)}{2x} =\dfrac{x-1}{x} =\dfrac{x}{x}-\dfrac{1}{x}=1-\dfrac{1}{x}[/tex]
