Question

Aduceti la forma cea mai simpla expresia:
(X supra x²-x + x+2 supra 2+x-2x²- x³ + x²supra x²+x) · (1-1supra x) , x∈R/(-2,-1,0,1)
Va rog urgent.

Answer 1

x/x(x-1) +(x+2)/[(2+x)-x² ·(2+x) + x² /x(x+1)·(x-1)/x =
= 1/(x-1) +(x+2)/(2+x)(1-x²) + (x-1)/(x+1)=
=1/(x-1) - (x+2)/(2+x)(x-1)(x+1) + (x-1)/(x+1) = 1/(x-1) - 1/(x+1)(x-1) +(x-1)/(x+1) =
= (x+1 - 1 + x² -2x+1)/(x+1)(x-1) = (x² -x +1)/(x+1)(x-1)