JAMB 1995 · UME · Q8

Simplify $\dfrac{\sqrt{12} - \sqrt3}{\sqrt{12} + \sqrt3}$ .

Worked solution (try it first)

Take out the square factor: $\sqrt{12} = \sqrt4 \times \sqrt3$ , which is $2\sqrt3$ .
Top: $2\sqrt3 - \sqrt3 = \sqrt3$ .
Bottom: $2\sqrt3 + \sqrt3 = 3\sqrt3$ .
So the value is $\dfrac{\sqrt3}{3\sqrt3} = \frac13$ , option A.