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WAEC Further Mathematics 2018 Paper

Question : 1

Total: 40

Simplify

\;\frac{\sqrt{3}}{\sqrt{3}-1} + \;\frac{\sqrt{3}}{\sqrt{3}+1}

Solution:

Concept:

Combine the two fractions over a single common denominator and simplify the resulting surd expression.

Explanation:

Take the common denominator

(\sqrt{3} - 1)(\sqrt{3} + 1)

\frac{\sqrt{3}}{\sqrt{3} - 1} + \frac{\sqrt{3}}{\sqrt{3} + 1} = \frac{\sqrt{3}(\sqrt{3} + 1) + \sqrt{3}(\sqrt{3} - 1)}{(\sqrt{3} - 1)(\sqrt{3} + 1)}

Expand the numerator:

\sqrt{3}(\sqrt{3} + 1) + \sqrt{3}(\sqrt{3} - 1) = (3 + \sqrt{3}) + (3 - \sqrt{3}) = 6

Simplify the denominator using the difference of two squares:

(\sqrt{3} - 1)(\sqrt{3} + 1) = (\sqrt{3})^2 - 1^2 = 3 - 1 = 2

So the expression becomes:

\frac{6}{2} = 3

Answer:

3

(Option B)

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