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