Explicație pas cu pas:
(x+2)(x²+4x+4)-x-2=(x+2)(x+2)²-1(x+2)=
(x+2)[(x+2)²-1]=(x+2)(x+2+1)(x+2-1)=
(x+1)(x+2)(x+3)
E(x)=(x+1)(x+2)(x+3)/x²+5x+6 =>
E(x)=(x+1)(x+2)(x+3)/(x+2)(x+3) =>
E(x)=x+1
E(n) =n+1 si cum n€N => n+1€N deci
E(n)€N
