$x=\large\frac{1}{2}$$ \bigg(\sqrt 3+\large\frac{1}{\sqrt 3} \bigg)$ then $\large\frac{\sqrt {x^2-1}}{x-\sqrt {x^2-1}}$ is equal to :

Question

\[\begin {array} {1 1} (a)\;1 & \quad (b)\;2 \\ (c)\;3 & \quad (d)\;\frac{1}{2} \end {array}\]