Question

Избавьтесь от иррациональности в знаменателе

Answer 1

$\displaystyle\bf\\5)\\\\\frac{1}{2\sqrt{5} -\sqrt{7} } =\frac{1\cdot(2\sqrt{5} +\sqrt{7} )}{(2\sqrt{5} -\sqrt{7})\cdot(2\sqrt{5} +\sqrt{7} )} =\\\\\\=\frac{2\sqrt{5} +\sqrt{7} }{(2\sqrt{5} )^{2} -(\sqrt{7})^{2} } =\frac{2\sqrt{5} +\sqrt{7} }{20-7} =\frac{2\sqrt{5} +\sqrt{7} }{13}$

$\displaystyle\bf\\6)\\\\\frac{1}{\sqrt{2} +\sqrt{3} } =\frac{1\cdot(\sqrt{2} -\sqrt{3} )}{(\sqrt{2} +\sqrt{3})\cdot(\sqrt{2} -\sqrt{3} )} =\\\\\\=\frac{\sqrt{2} -\sqrt{3} }{(\sqrt{2} )^{2} -(\sqrt{3})^{2} } =\frac{\sqrt{2} -\sqrt{3} }{2-3} =\frac{\sqrt{2} -\sqrt{3} }{-1} =\sqrt{3} -\sqrt{2}$