đk : xkhác -1 ; 1 ; 1/2
\(A=\dfrac{3-3x+x+1-8}{\left(1-x\right)\left(x+1\right)}:\dfrac{1-2x}{x^2-1}=\dfrac{-2x-4}{\left(1-x\right)\left(x+1\right)}:\dfrac{1-2x}{x^2-1}\)
\(=\dfrac{2x+4}{\left(x-1\right)\left(x+1\right)}:\dfrac{1-2x}{x^2-1}=\dfrac{2x+4}{1-2x}\)
\(=\left(\dfrac{3}{x+1}-\dfrac{1}{x-1}+\dfrac{8}{\left(x-1\right)\left(x+1\right)}\right)\cdot\dfrac{x^2-1}{1-2x}\)
\(=\dfrac{3x-3-x-1+8}{\left(x-1\right)\left(x+1\right)}\cdot\dfrac{\left(x-1\right)\left(x+1\right)}{-2x+1}\)
\(=\dfrac{2x+4}{-2x+1}=\dfrac{-2x-4}{2x-1}\)
ĐKXĐ:\(x\ne\pm1,x\ne\dfrac{1}{2}\)
\(A=\left(\dfrac{3}{x+1}+\dfrac{1}{1-x}-\dfrac{8}{1-x^2}\right):\dfrac{1-2x}{x^2-1}\)
\(\Rightarrow A=\left(\dfrac{3}{x+1}-\dfrac{1}{x-1}+\dfrac{8}{x^2-1}\right).\dfrac{x^2-1}{1-2x}\)
\(\Rightarrow A=\left(\dfrac{3\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}-\dfrac{x+1}{\left(x-1\right)\left(x+1\right)}+\dfrac{8}{\left(x-1\right)\left(x+1\right)}\right).\dfrac{x^2-1}{1-2x}\)
\(\Rightarrow A=\dfrac{3x-3-x-1+8}{\left(x-1\right)\left(x+1\right)}.\dfrac{x^2-1}{1-2x}\)
\(\Rightarrow A=\dfrac{2x+4}{x^2-1}.\dfrac{x^2-1}{1-2x}\)
\(\Rightarrow A=\dfrac{2x+4}{1-2x}\)
