Question

Arătati ca E(x)=(x supra x+2 +1 supra x^2-4)(x+1 supra x-1 +2x+5 supra 1-x^2):(1 supra x+1 -1 supra 2x) =2x

Answer 1

E(x)=[x/(x+2) +1/(x²-4)]×[(x+1)/(x-1) +(2x+5)/(1-x²)]:[1/( x+1) -1/2x] =
= [(x²-2x+1)/(x²-4)]×[(x+1)/(x-1) -(2x+5)/(x²-1)]:(2x-x-1)/2x( x+1) =
= (x-1)²/(x²-4) ×(x²+2x+1 -2x-5)/(x²-1)]:(2x-x-1)/2x( x+1) =
= (x-1)²/(x²-4) × (x²-4)/(x²-1):(x-1)/2x( x+1) =
= (x-1)/(x+1) ×2x( x+1)/(x-1) =
= 2x