\(\frac{4}{2 \sqrt{7}+ \sqrt{6} }\)
Multiply denominator and numerator of fraction by conjugate (2√7 -6)
=\(\frac{4(2 \sqrt{7})(- \sqrt{6}) }{(2 \sqrt{7} + \sqrt{6})(2 \sqrt{7} - \sqrt{6} ) }\)
Expand using distributive property
= \(\frac{8 \sqrt{7}- 4 \sqrt{6} }{28-2 \sqrt{42}+2 \sqrt{42} -6 }\)
Collect like terms to simplify
=\(\frac{8 \sqrt{7}-4 \sqrt{6} }{22}\)
