Question

Rationalise the denominator of √3-√4 ----------- √3+√4-√7

Answer 1

$\frac{\sqrt3-\sqrt4}{\sqrt3+\sqrt4-\sqrt7}=-\frac{2-\sqrt3}{2+\sqrt3-\sqrt7}\\\\=-\frac{2-\sqrt3}{2+\sqrt3-\sqrt7}*\frac{2-\sqrt3+\sqrt7}{2+\sqrt3+\sqrt7}\\\\=-\frac{(2-\sqrt3)^2+2\sqrt7-\sqrt{21}}{(2+\sqrt3)^2-7}\\\\=-\frac{7-4\sqrt3+2\sqrt7-\sqrt{21}}{7+4\sqrt3-7}\\\\=-\frac{(7-4\sqrt3+2\sqrt7-\sqrt{21})\sqrt3}{4\sqrt3*\sqrt3}\\\\=-\frac{7\sqrt3-12+2\sqrt{21}-3\sqrt7}{12}$