Biểu thức \(N\) thỏa mãn \(N:\dfrac{x^2+x+1}{2x+2}=\dfrac{x+1}{x^3-1}\) là
\(\dfrac{1}{2\left(x-1\right)}.\)\(\dfrac{1}{x-1}.\)\(\dfrac{1}{2\left(x+1\right)}.\)\(\dfrac{1}{2\left(1-x\right)}.\)Hướng dẫn giải:Ta có \(N:\dfrac{x^2+x+1}{2x+2}=\dfrac{x+1}{x^3-1}\)
\(\Leftrightarrow N=\dfrac{x+1}{x^3-1}.\dfrac{x^2+x+1}{2x+2}=\dfrac{x+1}{\left(x-1\right)\left(x^2+x+1\right)}.\dfrac{x^2+x+1}{2\left(x+1\right)}=\dfrac{1}{2\left(x-1\right)}.\)