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Rationalize the denominator of the expression \(\frac{6 + 2\sqrt{5}}{4 - 3\sqrt{6}}\)

Mathematics
JAMB 1979

Rationalize the denominator of the expression \(\frac{6 + 2\sqrt{5}}{4 - 3\sqrt{6}}\)

  • A. \(\frac{12+ 4\sqrt{5 + 7} 5 + 6\sqrt{3}}{39}\)
  • B. \(\frac{-(24 + 18\sqrt{6} + 8\sqrt{5} + 6\sqrt{30})}{38}\)
  • C. \(\frac{24 + 3\sqrt{6 + 8} 5 + 6\sqrt{30}}{19}\)
  • D. \(\frac{-15 + 3\sqrt{5 + 18} 5 + 6\sqrt{30}}{36}\)
  • E. \(\frac{-(12 + 4\sqrt{5} +9\sqrt{6} + 3\sqrt{30})}{19}\)
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Correct Answer: Option B
Explanation

Rationalize using the reciprocal of the denominator to multiply through 

(i.e. Multiply both numerator and denominator using \(4 + 3\sqrt{6}\) )

Watch your signs in the course of this.

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