Question

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

Answer 1

\(=\dfrac{\left(x+2\right)^2-\left(x-2\right)^2+8.2}{2\left(x-2\right)\left(x+2\right)}.\dfrac{x-2}{4}=\dfrac{8x+16}{8\left(x+2\right)}=\dfrac{8\left(x+2\right)}{8\left(x+2\right)}=1\)