Question

Упростить выражение

Answer 1

$\dfrac{2\sqrt{70}-2\sqrt{28}}{2\sqrt{35}-3\sqrt{14}} = \dfrac{2\sqrt{7\cdot10}-2\sqrt{7\cdot4}}{2\sqrt{7\cdot5}-3\sqrt{7\cdot2}} =\dfrac{\sqrt{7}(2\sqrt{10}-2\sqrt{4})}{\sqrt{7}(2\sqrt{5}-3\sqrt{2})} =\\ = \dfrac{2\sqrt{10}-4}{2\sqrt{5}-3\sqrt{2}} = \dfrac{(2\sqrt{10}-4)(2\sqrt{5}+3\sqrt{2})}{(2\sqrt{5}-3\sqrt{2})(2\sqrt{5}+3\sqrt{2})} =$

$=\dfrac{4\sqrt{50}-8\sqrt{5}+6\sqrt{20}-12\sqrt{2}}{20-18} = \dfrac{20\sqrt{2}-8\sqrt{5}+12\sqrt{5}-12\sqrt{2}}{2} =\\ =\dfrac{8\sqrt{2}+4\sqrt{5}}{2} =4\sqrt{2}+2\sqrt{5}.$