1. ĐKXĐ: \(x\ne0;x\ne2\)
Ta có: \(A=\left(\dfrac{x^2-2x}{2x^2+8}-\dfrac{2x^2}{8-4x+2x^2-x^3}\right)\left(1-\dfrac{1}{x}-\dfrac{2}{x^2}\right)\)
\(A=\left[\dfrac{x\left(x-2\right)}{2\left(x^2+4\right)}-\dfrac{2x^2}{4\left(2-x\right)+x^2\left(2-x\right)}\right]\left(\dfrac{x^2-x-2}{x^2}\right)\)
\(A=\left[\dfrac{x\left(x-2\right)}{2\left(x^2+4\right)}-\dfrac{2x^2}{\left(4+x^2\right)\left(2-x\right)}\right]\left(\dfrac{x^2-x-2}{x^2}\right)\)
\(A=\left[\dfrac{x\left(x-2\right)}{2\left(x^2+4\right)}+\dfrac{2x^2}{\left(4+x^2\right)\left(x-2\right)}\right]\left(\dfrac{x^2-x-2}{x^2}\right)\)
\(A=\dfrac{x\left(x-2\right)^2+2.2x^2}{2\left(x^2+4\right)\left(x-2\right)}.\dfrac{\left(x^2-2x\right)+\left(x-2\right)}{x^2}\)
\(A=\dfrac{x\left(x^2-4x+4\right)+4x^2}{2\left(x^2+4\right)\left(x-2\right)}.\dfrac{\left(x+1\right)\left(x-2\right)}{x^2}\)
\(A=\dfrac{\left(x^3+4x\right)\left(x+1\right)\left(x-2\right)}{2x^2\left(x^2+4\right)\left(x-2\right)}\)
\(A=\dfrac{x\left(x^2+4\right)\left(x+1\right)\left(x-2\right)}{2x^2\left(x^2+4\right)\left(x-2\right)}\)
\(A=\dfrac{x+1}{2x}\)
