Question

Aduceti la o forma mai simpla expresia :

E(x)=2x+1/x-1 : (1 - 3x²/1 -x²)

Answer 1

E(x)=(2x+1)/(x-1) : (1 - 3x²)/(1 -x²)=
=(2x+1)/(x-1) : ( 3x²-1)/(x²-1)=
=(2x+1)/(x-1) × (x-1)(x+1)/(3x²-1)=
=(2x+1)/1 × (x+1)/(3x²-1)=
=(2x+1)(x+1)/(3x²-1)=
=(2x²+x+2x+1)/(3x²-1)=
=(2x²+3x+1)/(3x²-1)=
=(2x²+2x+x+1)/(3x²-1)=
=[2x(x+1)+(x+1)]/(3x²-1)=
=(x+1)(2x+1)/(x√3-1)(x√3+1)