If $\tan^{-1}\large\frac{1}{a-1}$$=\tan^{-1}x+\tan^{-1}(x+1)=\tan^{-1}3x$ is

Question

$\begin{array}{1 1}(a)\;\large\frac{a}{2}&(b)\;a^3\\(c)\;a^2-a+1&(d)\;a^2+a-1\end{array}$