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