Question

сократите дробь и найдите значение выражения

Answer 1

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

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