\(\dfrac{1}{x+1}-\dfrac{5}{x-2}=\dfrac{15}{\left(x+1\right)\left(2-x\right)}\left(x\ne-1;x\ne2\right)\\ \Leftrightarrow x-2-5\left(x+1\right)=-15\\ \Leftrightarrow x-2-5x-5=-15\\ \Leftrightarrow-4x=-8\\ \Leftrightarrow x=2\left(\text{loại}\right)\\ \text{Vậy }S=\varnothing\\ \dfrac{x-1}{x+2}-\dfrac{x}{x-2}=\dfrac{5x-2}{4-x^2}\left(x\ne\pm2\right)\\ \Leftrightarrow\left(x-1\right)\left(x-2\right)-x\left(x+2\right)=2-5x\\ \Leftrightarrow x^2-3x+2-x^2-2x=2-5x\\ \Leftrightarrow0x=0\\ \Leftrightarrow x\in R\\ \text{Vậy }S=R\backslash\left\{-2;2\right\}\\ \dfrac{x+5}{x^2-5x}-\dfrac{x-5}{2x^2+10x}=\dfrac{x+25}{2x^2-50}\left(x\ne0;x\ne\pm5\right)\\ \Leftrightarrow2\left(x+5\right)^2-\left(x-5\right)^2=x+25\\ \Leftrightarrow2x^2+20x+50-x^2+10x-25=x+25\\ \Leftrightarrow x^2+29x=0\\ \Leftrightarrow x\left(x+29\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=0\left(\text{loại}\right)\\x=-29\end{matrix}\right.\\ \text{Vậy }S=\left\{-29\right\}\)
