If P : Q = 2 : \(\sqrt {3}\), then the value of (3P+Q) : (3P-2Q)?

\(\frac{1}{4}\)(7 + 3 \(\sqrt {3})\)

P : Q = 2 : \(\sqrt {3}\)

(3P+Q) : (3P-2Q) =  \(\frac{3 × 2 + \sqrt {3}}{3 × 2 - 2\sqrt {3}}\)

= \(\frac{6 + \sqrt {3}}{6 - 2\sqrt {3}}\) × \(\frac{6 + 2\sqrt {3} }{6 + 2\sqrt {3}}\)

= \(\frac{1}{24}\)(36 + 12\(\sqrt {3}\) + 6\(\sqrt {3}\) + 6)

=\(\frac{1}{24}\)(42 + 18\(\sqrt {3}\))

= \(\frac{1}{12}\)( 21 + 9\(\sqrt {3}\))

= \(\frac{1}{4}\)( 7 + 3\(\sqrt {3}\))