Answer the question on the basis of the information given below.
\[ P \# Q = \frac{P+PQ}{Q} \] \[ P \, \$ \, Q = \frac{P-PQ}{Q} \] \[ P \; ? \; Q = \frac{Q+PQ}{P} \] \[ P \, @ \, Q = \frac{Q-PQ}{P} \]
Find \(a \# b\), if \(a = (P \# Q + P \; ? \; Q)\), \(b = (P \, \$ \, Q + P \, @ \, Q)\) and \(P = 1\) and \(Q = 3\).