ĐKXĐ: x<>0;x<>1; x<>-1
Ta có: \(\frac{2}{\left(x+1\right)^3}\cdot\left(\frac{1}{x}+1\right)+\frac{1}{x^2+2x+1}\left(\frac{1}{x^2}+1\right)\)
\(=\frac{2}{\left(x+1\right)^3}\cdot\frac{x+1}{x}+\frac{1}{\left(x+1\right)^2}\cdot\frac{x^2+1}{x^2}\)
\(=\frac{2}{x\left(x+1\right)^2}+\frac{x^2+1}{x^2\left(x+1\right)^2}=\frac{2x+x^2+1}{x^2\left(x+1\right)^2}\)
\(=\frac{\left(x+1\right)^2}{x^2\left(x+1\right)^2}=\frac{1}{x^2}\)
Ta có: \(P=\left\lbrack\frac{2}{\left(x+1\right)^3}\cdot\left(\frac{1}{x}+1\right)+\frac{1}{x^2+2x+1}\left(\frac{1}{x^2}+1\right)\right\rbrack:\frac{x-1}{x^3}\)
\(=\frac{1}{x^2}\cdot\frac{x^3}{x-1}=\frac{x}{x-1}\)
rút gọn P 