Обчислити 62: (9-√19)+4: (√23+√19) – 7: (√23+4)

Решите задачу:

$\displaystyle \frac{62}{9-\sqrt{19}} +\frac{4}{\sqrt{23}+\sqrt{19}} -\frac{7}{\sqrt{23}+4} =\\\\\\ =\frac{62(9+\sqrt{19})}{(9-\sqrt{19})(9+\sqrt{19})} +\frac{4(\sqrt{23}-\sqrt{19})}{(\sqrt{23}+\sqrt{19})(\sqrt{23}-\sqrt{19})} -\frac{7(\sqrt{23}-4)}{(\sqrt{23}+4)(\sqrt{23}-4)} = \\\\\\ =\frac{62(9+\sqrt{19})}{81-19} +\frac{4(\sqrt{23}-\sqrt{19})}{23-19} -\frac{7(\sqrt{23}-4)}{23-16}= \\\\\\ =\frac{62(9+\sqrt{19})}{62} +\frac{4(\sqrt{23}-\sqrt{19})}{4} -\frac{7(\sqrt{23}-4)}{7}=$

$=9+\sqrt{19}+\sqrt{23}-\sqrt{19}-(\sqrt{23}-4) =9+\sqrt{23}-\sqrt{23}+4= 13$