\(A=\left(\dfrac{1}{x-1}+\dfrac{x}{\left(x-1\right)\left(x^2+x+1\right)}\cdot\dfrac{x^2+x+1}{x+1}\right)\cdot\dfrac{2x+1}{x^2+2x+1}\)
\(=\left(\dfrac{1}{x-1}+\dfrac{x}{\left(x-1\right)\left(x+1\right)}\right)\cdot\dfrac{2x+1}{\left(x+1\right)^2}\)
\(=\dfrac{x+1+x}{\left(x-1\right)\left(x+1\right)}\cdot\dfrac{2x+1}{x^2+2x+1}\)
\(=\dfrac{\left(2x+1\right)^2}{\left(x-1\right)\cdot\left(x+1\right)^3}\)
ĐKXĐ: \(x\ne\pm1\)
\(A=\left(\dfrac{1}{x-1}-\dfrac{x}{1-x^3}.\dfrac{x^2+x+1}{x+1}\right).\dfrac{2x+1}{x^2+2x+1}\)
\(A=\left[\dfrac{1}{x-1}+\dfrac{x}{\left(x-1\right)\left(x^2+x+1\right)}.\dfrac{x^2+x+1}{x+1}\right].\dfrac{2x+1}{x^2+2x+1}\)
\(A=\left[\dfrac{1}{x-1}+\dfrac{x}{\left(x-1\right)\left(x+1\right)}\right].\dfrac{2x+1}{x^2+2x+1}\)
\(A=\left[\dfrac{x+1}{\left(x+1\right)\left(x-1\right)}+\dfrac{x}{\left(x+1\right)\left(x-1\right)}\right].\dfrac{2x+1}{\left(x+1\right)^2}\)
\(A=\dfrac{2x+1}{\left(x+1\right)\left(x-1\right)}.\dfrac{2x+1}{\left(x+1\right)^2}\)
\(A=\dfrac{\left(2x+1\right)^2}{\left(x+1\right)^3.\left(x-1\right)}\)
Mình thấy đầu bài hơi sai sai có thể là (Nếu đầu bài trên đúng thì ko cần xem dưới naỳ):
ĐKXĐ: \(x\ne\pm1\)
\(A=\left(\dfrac{1}{x-1}-\dfrac{x}{1-x^3}.\dfrac{x^2+x+1}{x+1}\right):\dfrac{2x+1}{x^2+2x+1}\)
\(A=\left[\dfrac{1}{x-1}+\dfrac{x}{\left(x-1\right)\left(x^2+x+1\right)}.\dfrac{x^2+x+1}{x+1}\right]:\dfrac{2x+1}{x^2+2x+1}\)
\(A=\left[\dfrac{1}{x-1}+\dfrac{x}{\left(x-1\right)\left(x+1\right)}\right]:\dfrac{2x+1}{x^2+2x+1}\)
\(A=\left[\dfrac{x+1}{\left(x+1\right)\left(x-1\right)}+\dfrac{x}{\left(x+1\right)\left(x-1\right)}\right]:\dfrac{2x+1}{\left(x+1\right)^2}\)
\(A=\dfrac{2x+1}{\left(x+1\right)\left(x-1\right)}.\dfrac{\left(x+1\right)^2}{2x+1}\)
\(A=\dfrac{x+1}{x-1}\)
