Find the rational numbers a and b if (√6 - 2)/(√6 + 2) = a - b√6.

To clear a root from the bottom, multiply the top and the bottom by the same number: by $\sqrt{a}$ for $\dfrac{1}{\sqrt{a}}$, and by the conjugate $a - \sqrt{b}$ for $\dfrac{1}{a + \sqrt{b}}$. The value does not change.