Question

Упростить выражение

Answer 1

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

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