The equation of a curve is \(y=f(x)\) where \[f(x)=x-4-\frac{16(2x+1)^2}{x^2(x-4)}.\]

Write down the equations of the vertical and oblique asymptotes to the curve and show that the oblique asymptote is a tangent to the curve.

Show that the equation \(f(x)=0\) has a double root.

Sketch the curve.