[tex]\frac{ \sqrt{6}- \sqrt{7} }{ \sqrt{6}+ \sqrt{7} } \\
Multiply \ and \ divide \ by \ the \ conjugate. \\
=\frac{ \sqrt{6}- \sqrt{7} }{ \sqrt{6}+ \sqrt{7} } \times \ \frac{ \sqrt{6}- \sqrt{7} }{ \sqrt{6}- \sqrt{7} } \\
=[/tex]
[tex] \frac{( \sqrt{6}- \sqrt{7})^2 }{ \sqrt{6}^2 - \sqrt{7}^2 }} \\
=\frac{( \sqrt{6}- \sqrt{7})^2 }{-1} \\
=-( \sqrt{6}- \sqrt{7})^2 \\
= -( \sqrt{6}^2-2( \sqrt{6} \sqrt{7}+ \sqrt{7}^2 \\
=-(6 -2 \sqrt{42} +7) \\
=-6+2 \sqrt{42}-7 \\
=-13+2 \sqrt{42} \\
Answer: \ -13+2 \sqrt{42}[/tex]
