Question

Answer 1

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

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

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

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

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