NECO 2023 · Paper 1 · Q2

Rationalize $\dfrac{2}{\sqrt5 + \sqrt7}$ .

Worked solution (try it first)

Multiply the top and bottom by the conjugate of the bottom, $\sqrt7 - \sqrt5$ (same terms, sign changed).
The bottom becomes a difference of two squares: $(\sqrt7 + \sqrt5)(\sqrt7 - \sqrt5) = 7 - 5$ , which is 2.
So the fraction is $\dfrac{2(\sqrt7 - \sqrt5)}{2}$ , and the 2s cancel to leave $\sqrt7 - \sqrt5$ , option B.