Question

сократите дробь и найдите значение выражения

Answer 1

$1)\frac{\sqrt{10} -5}{\sqrt{10}-2 } =\frac{\sqrt{5*2}-(\sqrt{5})^{2}}{\sqrt{5*2} -(\sqrt{2} )^{2} }=\frac{\sqrt{5}(\sqrt{2} -\sqrt{5})}{\sqrt{2}(\sqrt{5} -\sqrt{2})}=-\frac{\sqrt{5} }{\sqrt{2} }=-\frac{\sqrt{5}*\sqrt{2}}{\sqrt{2}*\sqrt{2}}=-\frac{\sqrt{10} }{2}$

$\frac{3}{2\sqrt{7}+1 }-\frac{3}{2\sqrt{7}-1 }=\frac{6\sqrt{7}-3-6\sqrt{7}-3}{(2\sqrt{7}-1)(2\sqrt{7} +1) }=\frac{-6}{(2\sqrt{7})^{2}-1^{2}}=-\frac{6}{28-1}=\frac{6}{27} =\frac{2}{9}$