Question

Consideram E(x)=(3/2(x-1) -1/2(x+1) - 4/x la puterea a 2-a -1) totul impartit la :x-2/x la puterea a 2-a-2x+1.Aratati ca E(x)=x-1/x+1

Answer 1

E(x) = {3 / [2(x-1)] - 1 / [2(x+1)] - 4 / (x² - 1) }: (x-2) / (x-1)² =
= [3(x+1) - (x-1) - 8] / [2(x-1)(x+1)] · (x-1)² /(x-2)=
= ( 2x - 4) / [2(x-1) (x+1)] · (x-1)² /(x-2) = 2(x-2) / [2(x-1)(x+1)]· (x-1)² / (x-2) =
= (x-1)/(x+1)