Simplify \(\frac{2\sqrt{3} + 3\sqrt{5}}{3\sqrt{5} - 2\sqrt{3}}\)
A
\(\frac{19 + 4\sqrt{25}}{11}\)
B
\(\frac{19 + 4\sqrt{15}}{11}\)
C
\(\frac{19 + 2\sqrt{15}}{11}\)
D
\(\frac{19 + 2\sqrt{15}}{19}\)
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
\(\frac{(2\sqrt{3} + 3\sqrt{5})(3\sqrt{5} + 2\sqrt{3})}{(3\sqrt{5} - 2\sqrt{3})(3\sqrt{5} - 2\sqrt{3})}\)
= \(\frac{57 + 12\sqrt{15}}{33}\)
=\(\frac{19 + 4\sqrt{15}}{11}\)
Source: Myschool Past Questions Archive (Record #30793)