Fraction transformations

An improper fraction has numerator \(n\) and denominator \(d\). If \(1\) is subtracted from its numerator and \(1\) is added to its denominator, it becomes \(\frac{3}{2}\). If \(1\) is added to its numerator and its denominator is doubled, it becomes \(1\).

1. Form two equations in \(n\) and \(d\).
2. Solve the equations obtained in (a) to find \(n\) and \(d\).
3. Hence, state the original fraction in its simplest form.