Question

Square root of 6 minus square root of 7 divided by square root of 6 plus square root of 7

Answer 1

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