Salut,
[tex]E(x)=\dfrac{x^2-x}{x-1}-\left(\dfrac{x+1}{x-1}-\dfrac{x-1}{x+1}\right):\dfrac{4}{x^2-1}=\\\\=\dfrac{x(x-1)}{x-1}-\dfrac{(x+1)^2-(x-1)^2}{(x-1)(x+1)}\cdot\dfrac{x^2-1}{4}=
\\\\=x-\dfrac{x^2+2x+1-(x^2-2x+1)}{x^2-1}\cdot\dfrac{x^2-1}{4}=\\\\=x-\dfrac{x^2+2x+1-x^2+2x-1}{x^2-1}\cdot\dfrac{x^2-1}{4}=\\\\=x-\dfrac{4x}{x^2-1}\cdot\dfrac{x^2-1}{4}=x-x=0,[/tex]
ceea ce trebuia demonstrat.
Învață aducerea la același numitor, formulele de calcul prescurtat, simplificările, nu sunt deloc grele.
Green eyes.
