( √n / (√m+√n) - (√n-√m) / √n ) : ( √m / √n ) =
=((√n*√n) / (√n*(√m+√n)) - (√n-√m)(√m+√n) /√n*(√m+√n)) * (√n /√m ) =
= ( n - (n-m) ) / √n*(√m+√n) ) * ( √n / √m ) =
= ( m / √n*(√m+√n) ) * ( √n / √m ) =
= √m / (√m+√n)
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( √n / (√m+√n) - (√n-√m) / √n ) : ( √m / √n ) =
=((√n*√n) / (√n*(√m+√n)) - (√n-√m)(√m+√n) /√n*(√m+√n)) * (√n /√m ) =
= ( n - (n-m) ) / √n*(√m+√n) ) * ( √n / √m ) =
= ( m / √n*(√m+√n) ) * ( √n / √m ) =
= √m / (√m+√n)