For positive numbers $x$ and $y$ the operation $\spadesuit (x,y)$ is defined as 
\[\spadesuit (x,y) = x-\dfrac{1}{y}\]
What is $\spadesuit (2,\spadesuit (2,2))$?
$\mathrm{(A)}\ \dfrac{2}{3} \qquad \mathrm{(B)}\ 1 \qquad \mathrm{(C)}\ \dfrac{4}{3} \qquad \mathrm{(D)}\ \dfrac{5}{3} \qquad \mathrm{(E)}\ 2$
$\spadesuit (2,2) =2-\frac{1}{2} =\frac{3}{2}$. Then, $\spadesuit \left(2,\frac{3}{2}\right)$ is $2-\frac{1}{\frac{3}{2}} = 2- \frac{2}{3} = \frac{4}{3}$
The answer is $\boxed{C}$