Question

Перепишите данное выражение,заменив знак : чертой дроби: а) mn: (m+n)-mn: (m-n) б) (y+(y-1): (y+-(y+1): (y-1))

Answer 1

$\frac{mn}{(m+n)}-\frac{mn}{(m-n)}\\ \frac{y+(y-1)}{(y+1)}*\frac{y-(y+1)}{(y-1)}$

Answer 2

Перепишем заменив знаки :  знаком /.

Заодно сократим выражения

а) mn:(m+n)-mn:(m-n) =mn/(m+n)-mn/(m-n) =mn(1/(m+n)-1/(m-n)) =
=mn((m-n+m+n)/((m+n)(m-n)) = mn*2m/(m^2-n^2) =2nm^2/(m^2-n^2)

б) (y+(y-1):(y+1))(y-(y+1):(y-1)) = (y+(y-1)/(y+1))* (y-(y+1)/(y-1))=
=[(y*(y+1)+y-1)/(y+1)]*[(y*(y-1)+(y-1))/(y-1)]=
= [(y^2+2y-1)/(y+1)]*[(y^2-1)/(y-1)]=
=(y^2+2y-1)*(y^2-1)/((y+1)/(y-1))=(y^2+2y-1)*(y^2-1)/(y^2-1)=
=y^2+2y-1