Kết quả rút gọn biểu thức \(A=\dfrac{x^2+1}{3x}:\dfrac{x^2+1}{x-1}:\dfrac{x^3-1}{x^2+x}:\dfrac{x^2+2x+1}{x^2+x+1}\) là
\(\dfrac{3}{x+1}.\)\(\dfrac{1}{3\left(x+1\right)}.\)\(-\dfrac{1}{3\left(x+1\right)}.\)\(-\dfrac{3}{x+1}.\)Hướng dẫn giải:\(A=\dfrac{x^2+1}{3x}:\dfrac{x^2+1}{x-1}:\dfrac{x^3-1}{x^2+x}:\dfrac{x^2+2x+1}{x^2+x+1}\)
\(=\dfrac{x^2+1}{3x}.\dfrac{x-1}{x^2+1}.\dfrac{x^2+x}{x^3-1}.\dfrac{x^2+x+1}{x^2+2x+1}\)
\(=\dfrac{x^2+1}{3x}.\dfrac{x-1}{x^2+1}.\dfrac{x\left(x+1\right)}{\left(x-1\right)\left(x^2+x+1\right)}.\dfrac{x^2+x+1}{\left(x+1\right)^2}\)
\(=\dfrac{1}{3\left(x+1\right)}.\)
