Aduceti la forma cea mai simpla: [tex]a) \frac{x-1}{ x^{2}-x+1 }- \frac{2x-2}{ x^{3}+1 }; [/tex] [tex]b) \frac{2x-1}{ x^{3}-1 }- \frac{x}{x-1}+1.[/tex]
a) numitorul comun x³+1=(x+1)(x²-x+1) [(x-1)(x+1)-2x+2]/(x³+1)=(x²-1-2x+2)/(x³+1)=(x²-2x+1)/(x³+1)=(x-1)²/(x³+1) b) x³-1=(x-1)(x²+x+1) [2x-1-x(x²+x+1)+x³-1]/(x³-1)=(2x-1-x³-x²-x+x³-1)/(x³-1)=(-x²+x-2)/(x³-1)=(x²-x+2)/(1-x³)
