Question

fie E(x)= x^2-4/x^2-4x+4, unde x apartine R \ {2}. aratati ca E(x)- 4/x-2 apartine N*, oricare ar fi x apartine R \ {2}.

Answer 1

$\it E(x )= \dfrac{x^2-4}{x^2-4x+4} =\dfrac{(x-2)(x+2)}{(x-2)^2} =\dfrac{x+2}{x-2}$

$\it E(x) -\dfrac{4}{x-2} = \dfrac{x+2}{x-2} - \dfrac{4}{x-2} =\dfrac{x+2-4}{x-2} =\dfrac{x-2}{x-2} =1 \in\mathbb{N}^*$

Answer 2

Nu stiu daca textul exercitiului de mai sus este acesta, deoarece nu rezulta din enunt, adevarata ordine a operetiilor.