ĐKXĐ: \(x\notin\left\{-5;1;-1;-2\right\}\)
\(D=\dfrac{x^3+2x^2-x-2}{2x+10}\cdot\left(\dfrac{1}{x-1}-\dfrac{2}{x+1}+\dfrac{1}{x+2}\right)\)
\(=\dfrac{x^2\left(x+2\right)-\left(x+2\right)}{2\left(x+5\right)}\cdot\dfrac{\left(x+1\right)\left(x+2\right)-\left(x-1\right)\left(x+2\right)+\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)\left(x+2\right)}\)
\(=\dfrac{\left(x+2\right)\left(x^2-1\right)}{2\left(x+5\right)}\cdot\dfrac{x^2+3x+2-\left(x^2+x-2\right)+x^2-1}{\left(x-1\right)\left(x+1\right)\cdot\left(x+2\right)}\)
\(=\dfrac{2x^2+3x+1-x^2-x+2}{2\left(x+5\right)}\)
\(=\dfrac{2x^2+2x+3}{2\left(x+5\right)}\)
