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