Can we sketch this curve with an oblique asymptote?

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

1. 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.

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

3. Sketch the curve.