Question

9/5-√7+22/7+√5-1/√7+√5

Answer 1

$\displaystyle\bf\\\frac{9}{5-\sqrt{7} } +\frac{22}{7+\sqrt{5} } -\frac{1}{\sqrt{7} +\sqrt{5} } =\\\\\\=\frac{9\cdot(5+\sqrt{7} )}{(5-\sqrt{7})\cdot(5+\sqrt{7} ) } +\frac{22\cdot(7-\sqrt{5} )}{(7+\sqrt{5} )(7-\sqrt{5} )} -\frac{1\cdot(\sqrt{7} -\sqrt{5}) }{(\sqrt{7} +\sqrt{5} )(\sqrt{7} -\sqrt{5} )} =\\\\\\=\frac{9\cdot(5+\sqrt{7} )}{25-7 } +\frac{22\cdot(7-\sqrt{5} )}{49-5} -\frac{1\cdot(\sqrt{7} -\sqrt{5}) }{7-5} =$

$\displaystyle\bf\\=\frac{9\cdot(5+\sqrt{7} )}{18 } +\frac{22\cdot(7-\sqrt{5} )}{44} -\frac{1\cdot(\sqrt{7} -\sqrt{5}) }{2} =\\\\\\=\frac{5+\sqrt{7} }{2} +\frac{7-\sqrt{5} }{2} -\frac{\sqrt{7} -\sqrt{5} }{2} =\\\\\\=\frac{5+\sqrt{7}+7-\sqrt{5}-\sqrt{7} +\sqrt{5} }{2} =\frac{12}{2} =6$