(((x^2/4)+1)/(((x)/2)+1))
$$\dfrac{\frac{x^2}{4}+1}{\frac{x}{2}+1}\\\\\\ =\dfrac{\frac{x^2+4}{4}}{\frac{x+2}{2}}\\\\\\ =\frac{x^2+4}{4}\div \frac{x+2}{2}\\\\ =\frac{x^2+4}{4}\times \frac{2}{x+2}\\\\ =\frac{x^2+4}{2(x+2)}$$