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. \(\frac{-(24 + 18\sqrt{6} + 8\sqrt{5} + 6\sqrt{30})}{39}\) 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. \(\frac{-(12 + 4\sqrt{5} +9\sqrt{6} + 3\sqrt{30})}{19}\)
Correct Answer: E
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.
