Question

Se considera expresia E(x)=x²+4x+4/x(x+2) : (1+2/x), unde x este numar real x≠-2 si x≠0. Aratati ca E(x)=1 pentru orice numar real, x≠-2 si x≠0.

Answer 1

E (x ) = ( x + 2)² · x  /  x·( x +2) ·( x +2) 
E ( x ) = ( x + 2)² · x  /  x · ( x +2)²
E(x) = 1 

Answer 2

(x²+4x+4)/[x*x/x+2/x*(x+2)]=(x²+4x+4)/[x*(x+2)/x*(x+2)]=
=[(x+2)(x+2)]/[x*(x+2)/x*(x+2)]=(x+2)²/[x*(x+2)/x*(x+2)]=
=[x(x+2)²]/[x*(x+2)(x+2)]=(x+2)²/[(x+2)(x+2)]=(x+2)²(x+2)⁻²=
=(x+2)²⁻²=(x+2)⁰=>
=>(x+2)⁰=1  raspunsul deci este 1
{x∈R:x≠-2 si x≠0}
E(x)=1