The curves \(C_1\) and \(C_2\) have equations \[y=\frac{ax}{x+2}\qquad\text{and}\qquad y=\frac{x^2+(a+4)x+2a+8}{x+2}\] respectively, where \(a\) is a constant.
Find the set of values of \(a\) such that \(C_1\) and \(C_2\) do not intersect for all real values of \(x\).[3]
It is now given that \(0<a<4\).
Find, in terms of \(a\), the coordinates of the stationary points of \(C_2\).[4]
Sketch \(C_1\) and \(C_2\) on a single diagram and give the equations of the asymptotes, in terms of \(a\) where appropriate.[5]
Hence solve the inequality \(\displaystyle \frac{ax}{x+2}>\frac{x^2+(a+4)x+2a+8}{x+2}\).[1]