Question

[Nguyễn Thiện Nhân]

Thực hiện phép tính: (\(\dfrac{2x-1}{2x+1}-\dfrac{2x+1}{2x-1}\left(\right):\dfrac{8x}{8x-4}\)

Answer 1

[Thanh Trà]

\(\left(\dfrac{2x-1}{2x+1}-\dfrac{2x+1}{2x-1}\right):\dfrac{8x}{8x-4}\)

\(=(\dfrac{\left(2x-1\right)^2}{4x^2-1}-\dfrac{\left(2x+1\right)^2}{4x^2-1}):\dfrac{8x}{4\left(2x-1\right)}\)

\(=\left(\dfrac{4x^2-4x+1}{4x^2-1}-\dfrac{4x^2+4x+1}{4x^2-1}\right):\dfrac{8x}{4\left(2x-1\right)}\)

\(=\dfrac{4x^2-4x+1-4x^2-4x-1}{4x^2-1}:\dfrac{8x}{4\left(2x-1\right)}\)

\(=\dfrac{-8x}{4x^2-1}:\dfrac{8x}{4\left(2x-1\right)}\)

\(=\dfrac{-8x.4\left(2x-1\right)}{8x\left(2x-1\right)\left(2x+1\right)}\)

\(=\dfrac{-8x.4}{8x\left(2x+1\right)}\)

\(=\dfrac{-4}{2x+1}\)