A number $x$ is $2$ more than the product of its [reciprocal](https://artofproblemsolving.com/wiki/index.php/Reciprocal) and its additive [inverse](https://artofproblemsolving.com/wiki/index.php/Inverse). In which [interval](https://artofproblemsolving.com/wiki/index.php/Interval) does the number lie?
$\textbf{(A) }\ -4\le x\le -2\qquad\textbf{(B) }\ -2 < x\le 0\qquad\textbf{(C) }0$ $< x \le 2 \qquad \textbf{(D) }\ 2 < x\le 4\qquad\textbf{(E) }\ 4 < x\le 6$
We can write our [equation](https://artofproblemsolving.com/wiki/index.php/Equation) as 
$x= \left(\frac{1}{x} \right) \cdot (-x) +2 = -1+2 = 1$.
Therefore, $\boxed{\textbf{(C) }0 < x\le 2}$.