If $$c - d = \frac{{c + d}}{5} = \frac{{cd}}{3}$$    and c, d ≠ 0 then what is the value of cd?

$$\eqalign{ & \because \,c - d = \frac{{c + d}}{5} = \frac{{cd}}{3} \cr & \Rightarrow 5c - 5d = c + d \cr & \Rightarrow 4c = 6d \cr & \Rightarrow \boxed{\frac{c}{d} = \frac{3}{2}} \cr & \Rightarrow c = \frac{3}{2}d\,......\,\left( 1 \right) \cr & \because \,\frac{{c + d}}{5} = \frac{{cd}}{3} \cr & \Rightarrow \frac{{\frac{3}{2}d + d}}{5} = \frac{{\frac{3}{2}{d^2}}}{3} \cr & \Rightarrow \frac{{5d}}{2} \times \frac{1}{5} = \frac{1}{2}{d^2} \cr & \Rightarrow d = 1 \cr & {\text{From equation }}\left( 1 \right) \cr & \boxed{c = \frac{3}{2}} \cr & \therefore \,\boxed{cd = \frac{3}{2}} \cr} $$