WAEC Further Mathematics 2023 Paper

Concept:Rationalising the denominator helps to express the fraction without a square root in the denominator.Explanation:Write the given expression as $\frac{3}{3 - \sqrt{6}}$.Multiply the numerator and the denominator by the conjugate $3 + \sqrt{6}$:$\frac{3}{3 - \sqrt{6}} \times \frac{3 + \sqrt{6}}{3 + \sqrt{6}}$Multiply the numerators: $3(3 + \sqrt{6})$Multiply the denominators using $(a - b)(a + b) = a^2 - b^2$:$(3)^2 - (\sqrt{6})^2 = 9 - 6 = 3$So the expression becomes $\frac{3(3 + \sqrt{6})}{3}$.Cancel the common factor 3 from the numerator and denominator:Therefore, $\frac{3}{3 - \sqrt{6}} = 3 + \sqrt{6}$.Answer:$3 + \sqrt{6}$, which is option C.