Rút gọn các biểu thức sau: b) x^3+1/ 1-x^3+ x/ x-1- x+1/ x^2+x++1 ;

Trả lời

b, $\frac{x^3+1}{1-x^3}+\frac{x}{x-1}-\frac{x+1}{x^2+x+1}=\frac{x^3+1}{(1-x)(x^2+x+1)}-\frac{x}{1-x}-\frac{x+1}{x^2+x+1}$

$$\begin{gathered} =\frac{x^3+1-x(x^2+x+1)-(1-x)(x+1)}{(1-x)(x^2+x+1)}=\frac{x^3+1-x^3-x^2-x-1+x^2}{(1-x)(x^2+x+1)} \\ =\frac{-x}{1-x^3}=\frac{x}{x^3-1} \end{gathered}$$