Question

E(x)=[(1-x)/(1+x)]+[(1+x)/(1-x)]+4x/(x la patrat -1)

Answer 1

E(x)=[(1-x)/(1+x)]+[(1+x)/(1-x)]+4x/(x la patrat -1)=amplificam primul raport cu 1-x
                 al 2 cu              1+x
                    al 3 cu            -1

obtinem
(1-x) la patrat + (1+x) la patrat - 4x totul supra 1- x patrat

adica 1-2x+xpatrat + 1 +2x +xpatrat -4x totul supra 1- x patrat

adica 2-4x+2xpatrat totul supra 1- x patrat

adica 2(1-x)la patrat totul supra (1- x)(1+x)
adica 2(1-x)/(1+x)

Answer 2

E(x)=[(1-x)/(x+1)]+[(1+x)/-(x-1)]+4x/(x+1)(x-1)
E(x)=[(1-x)(x-1)-(1+x)(x+1)+4x)]/(x+1)(x-1)
E(x)=[(x-1-x²+x-x-x-x²-x+4x)]/(x+1)(x-1)
E(x)=(-2x²+3x-1)/(x+1)(x-1)
-(2x²-3x+1)=0
Δ=9-8=1
x1=(3-1)/4=2/4=1/2
x2=(3+1)/4=4/4=1
E(x)=-(2x-1)(x-1)(x+1)(x-1)=simplificam
E(x)=(1-2x)/(x+1)