Question

Спростите (√n/√m+√n-√n-√m/√n)/√m/√n

Answer 1

$( frac{ sqrt{n} }{sqrt{m}+sqrt{n} }- frac{ sqrt{n}- sqrt{m} }{sqrt{n} } ): frac{ sqrt{m} }{sqrt{n} }= frac{ sqrt{n}* sqrt{n}-( sqrt{n}- sqrt{m} )(sqrt{m}+sqrt{n}) }{(sqrt{m}+sqrt{n})sqrt{n} } * frac{ sqrt{n} }{sqrt{m} }= \ \ =frac{ n-( sqrt{n}- sqrt{m} )(sqrt{m}+sqrt{n}) }{sqrt{m}+sqrt{n} } * frac{ 1 }{sqrt{m} } =frac{ n-(n-m) }{sqrt{m}+sqrt{n} } * frac{ 1 }{sqrt{m} }= frac{ n-n+m }{sqrt{m}+sqrt{n} } * frac{ 1 }{sqrt{m} }=$
$frac{ n-n+m }{sqrt{m}+sqrt{n} } * frac{ 1 }{sqrt{m} }= frac{ m }{(sqrt{m}+sqrt{n})sqrt{m} }=frac{ m sqrt{m} }{(sqrt{m}+sqrt{n})m} = frac{ sqrt{m} }{sqrt{m}+sqrt{n}}$