A simplified expression with a missing input

8 written marks

For real \(x\), let \(\displaystyle R(x)=\frac{2x^2-5x-3}{x-3}\).

1. Factorise the numerator and state the domain of \(R\).

   [3]

2. Solve \(R(x)=0\).

   [2]

3. Find all real \(q\) for which \(R(x)=q\) has exactly one real solution. Give that solution in terms of \(q\).

   [3]

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