ĐKXĐ: \(x\notin\left\{2;-2;0;3\right\}\)
Ta có: \(P=\left(\dfrac{4x}{2+x}+\dfrac{8x^2}{4-x^2}\right):\left(\dfrac{x-1}{x^2-2x}-\dfrac{2}{x}\right)\)
\(=\left(\dfrac{4x\left(x-2\right)}{\left(x+2\right)\left(x-2\right)}-\dfrac{8x^2}{\left(x+2\right)\left(x-2\right)}\right):\left(\dfrac{x-1}{x\left(x-2\right)}-\dfrac{2\left(x-2\right)}{x\left(x-2\right)}\right)\)
\(=\dfrac{4x^2-8x-8x^2}{\left(x+2\right)\left(x-2\right)}:\dfrac{x-1-2x+4}{x\left(x-2\right)}\)
\(=\dfrac{-4x^2-8x}{\left(x+2\right)\left(x-2\right)}\cdot\dfrac{x\left(x-2\right)}{-x+3}\)
\(=\dfrac{-4x\left(x+2\right)}{x+2}\cdot\dfrac{x}{3-x}\)
\(=\dfrac{-4x^2}{3-x}\)
Để P<0 thì \(\dfrac{-4x^2}{3-x}< 0\)
mà \(-4x^2< 0\forall x\) thỏa mãn ĐKXĐ
nên 3-x<0
hay x>3
Kết hợp ĐKXĐ, ta được: x>3
Vậy: Để P<0 thì x>3
