Question

Answer 1

a: \(D=\left(\dfrac{x^2-2x}{2\left(x^2+4\right)}+\dfrac{2x^2}{x^3-2x^2+4x-8}\right)\cdot\dfrac{x^2-x-2}{x^2}\)

\(=\left(\dfrac{x^2-2x}{2\left(x^2+4\right)}+\dfrac{2x^2}{\left(x-2\right)\left(x^2+2\right)}\right)\cdot\dfrac{\left(x-2\right)\left(x+1\right)}{x^2}\)

\(=\dfrac{x\left(x-2\right)^2+4x^2}{2\left(x-2\right)\left(x^2+2\right)}\cdot\dfrac{\left(x-2\right)\left(x+1\right)}{x^2}\)

\(=\dfrac{x^3-4x^2+4x+4x^2}{2\left(x^2+2\right)}\cdot\dfrac{x+1}{x^2}=\dfrac{x\left(x^2+4\right)\cdot\left(x+1\right)}{2\left(x^2+2\right)}\)

b: D=0

=>x=0(loại) hoặc x=-1(loại)