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Simplify \(\frac{5+\sqrt{7}}{3+\sqrt{7}}\)

Mathematics
JAMB 2009

Simplify \(\frac{5+\sqrt{7}}{3+\sqrt{7}}\)

  • A. 17-√7
  • B. 4-√7
  • C. 15+√7
  • D. 7-√7
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Correct Answer: Option B
Explanation

\(\frac{5+\sqrt{7}}{3+\sqrt{7}}=\frac{5+\sqrt{7}}{3+\sqrt{7}}\times \frac{3-\sqrt{7}}{3-\sqrt{7}}\\
=\frac{(5+\sqrt{7})(3-\sqrt{7})}{3^2 - \sqrt{7}^2}\\
=\frac{15-5\sqrt{7}+3\sqrt{7}-7}{9-7}\\
=\frac{8-2\sqrt{7}}{2}\)
Factorize then divide by 2
\(=\frac{2(4-\sqrt{7}}{2}\\
=4-\sqrt{7}\)

There is an explanation video available below.


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Explanation Video

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