2025 MI P1 Q2

The diagram below shows the curve with equation \(y = \mathrm{f}(x)\) where \(\mathrm{f}(x) = \frac{x^2 + px + q}{x - 2}\) for some constants \(p\) and \(q\). The curve passes through the point with coordinates \((0, -1.5)\) and has asymptotes \(y = x - 1\) and \(x = r\) for some constant \(r\).

1. Write down the value of \(r\) and show that \(p = -3\) and \(q = 3\).[3]
2. Solve the inequality \(\mathrm{f}(x) > \frac{7}{2}\).[1]