Simplify \(\frac{\sqrt{3}}{\sqrt{3} - 1} + \frac{\sqrt{3}}{\sqrt{3} +1}\)
FURTHER MATHEMATICS
WAEC 2007
Simplify \(\frac{\sqrt{3}}{\sqrt{3} - 1} + \frac{\sqrt{3}}{\sqrt{3} +1}\)
- A. \(\frac{1}{2}\)
- B. \(\frac{1}{2}\sqrt{3}\)
- C. \(3\)
- D. \(2\sqrt{3}\)
Correct Answer: C. \(3\)
Explanation
\(\frac{\sqrt{3}}{\sqrt{3} - 1} + \frac{\sqrt{3}}{\sqrt{3} + 1}\)
= \(\frac{\sqrt{3}(\sqrt{3} + 1) + \sqrt{3}(\sqrt{3} - 1)}{(\sqrt{3} - 1)(\sqrt{3} + 1)}\)
= \(\frac{6}{3 - 1} \)
= 3
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