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
\(\frac{-(12 + 4\sqrt{5} +9\sqrt{6} + 3\sqrt{30})}{19}\)
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
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.
Source: Myschool Past Questions Archive (Record #32657)