Question

2)Se considera expresia E(x)= \frac{(2x+1)^2-(2x-1)^2 }{(x-1)^2-(x+1)^2} , unde x este numar real, x≠0. Aratati ca E(x)= -2 , pentru orice numar real x, x≠0

Answer 1

E(x)=[(2x+1)^2-(2x-1)^2]/[(x-1)^2-(x+1)^2]=[(2x+1-2x+1)*(2x+1+2x-1)]/[(x-1+x+1)*(x-1-x-1)]=(2*4x)/[2x*(-2)]=-8x/4x=-2
a^2-b^2=(a-b)*(a+b)

Answer 2

$\displaystyle E(x)= \frac{(2x+1)^2-(2x-1)^2 }{(x-1)^2-(x+1)^2} \\ E(x)= \frac{(2x)^2+2 \cdot 2x \cdot 1+1^2-[(2x)^2-2 \cdot 2x \cdot 1+1^2]}{x^2-2 \cdot x \cdot 1+1^2-(x^2+2 \cdot x \cdot 1+1^2)} \\ E(x)= \frac{4x^2+4x+1-(4x^2-4x+1)}{x^2-2x+1-(x^2+2x+1)} \\ E(x)= \frac{\not4x^2+4x+\not1-\not4x^2+4x-\not1}{\not x^2-2x+\not1-\not x^2-2x- \not1} \\ E(x)= \frac{4x+4x}{-2x-2x} \\ \\ E(x)= \frac{8x}{-4x} \\ \boxed{E(x)=-2}$