Question

Найдите значение выражения

Answer 1

$\frac{2}{3\sqrt{5} +1} -\frac{2}{3\sqrt{5}-1 }=\frac{2\cdot(3\sqrt{5}-1)-2\cdot(3\sqrt{5}+1) }{(3\sqrt{5} +1)(3\sqrt{5} -1)}=\frac{6\sqrt{5}-2-6\sqrt{5}-2}{(3\sqrt{5})^{2}-1^{2}} =\\\\=\frac{-4}{9\cdot5-1}=-\frac{4}{44}=\boxed{-\frac{1}{11}}$