ĐKXĐ: \(x\ne\pm1;x\ne0\)
\(B=\left[\dfrac{x^2}{x^2-1}-\dfrac{x^2}{x^2+1}\left(\dfrac{x}{x+1}+\dfrac{1}{x^2+x}\right)\right]:\dfrac{1}{x+1}\)\(=\left[\dfrac{x^2}{x^2-1}-\dfrac{x^2}{x^2+1}\left(\dfrac{x}{x+1}+\dfrac{1}{x\left(x+1\right)}\right)\right].\left(x+1\right)\)\(=\left[\dfrac{x^2}{x^2-1}-\dfrac{x^2}{x^2+1}.\dfrac{x^2+1}{x\left(x+1\right)}\right]\left(x+1\right)\)
\(=\left[\dfrac{x^2}{\left(x-1\right)\left(x+1\right)}-\dfrac{x}{x+1}\right]\left(x+1\right)\)
\(=\left[\dfrac{x^2}{\left(x-1\right)\left(x+1\right)}-\dfrac{x\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}\right]\left(x+1\right)\)\(=\dfrac{x^2-x^2+x}{\left(x-1\right)\left(x+1\right)}.\left(x+1\right)\)
\(=\dfrac{x}{x-1}\)
