JAMB 1989 · UME · Q10

Surds

Simplify $4 - \dfrac{1}{2 - \sqrt3}$ .

Worked solution (try it first)

Rationalise the fraction by multiplying the top and bottom by $2 + \sqrt3$ .
The bottom becomes $4 - 3 = 1$ , so $\dfrac{1}{2 - \sqrt3} = 2 + \sqrt3$ .
Subtract from 4: $4 - (2 + \sqrt3) = 2 - \sqrt3$ , option D.

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