Question

se considera expresia E(x)={x-1-x²supra x+2}:x-2 supra x+2,unde x este numar real,x≠-2 si x≠2.Aratati ca E(x)=1,pt orice numar real x,x≠-2 si x≠2.

Answer 1

E(x)=(x-1-x^2/x+2)*x+2/x-2
{(x-1)( x+2) - x^2/x+2}  *x+2/x-2
{x^2+2x-x-2-x^2/x+2}*x+2/x-2
x-2/x+2 * x+2/x-2
E(x)=1

Answer 2

E(x)= {x-1-x^2/x+2}*x+2/X-2
aducem la acelasi numitor si obtinem:
{(x-1) (x+2) -x^2/x+2}*x+2/x-2
{x^2+2x-x-2-x^2/x+2}*x+2/x-2
x-2/x+2 * x+2 /x-2=1