Rationalize the denominator:

$\dfrac{1}{(\sqrt{3} - 1)}$

Rationalizing on denominator,

$\Rightarrow \dfrac{1}{(\sqrt{3} - 1)} \times \dfrac{(\sqrt{3} + 1)}{(\sqrt{3} + 1)} \\[1em] \Rightarrow \dfrac{(\sqrt{3} + 1)}{(\sqrt{3})^2 - (1)^2} \\[1em] \Rightarrow \dfrac{(\sqrt{3} + 1)}{3 - 1} \\[1em] \Rightarrow \dfrac{(\sqrt{3} + 1)}{2} \\[1em]$

Hence, on rationalizing $\dfrac{1}{(\sqrt{3} - 1)} = \dfrac{(\sqrt{3} + 1)}{2}$.