Răspuns:
x/y=3/4 =>x=3y/4
y≠0
(2x+3y)/(4x+y)=
(2·3y/4+3y)/(4·3y/4+y)=
(6y/4+⁴⁾3y)/(12y/4+⁴⁾y)=
(6y/4+12y/4)/(12y/4+4y/4)=
(18y/4)/(16y/4)=
18y/4·4/16y=(18/16)⁽2=9/8
___________________
x/y=7/9=>x=7y/9
(x+2y)/(3x+y)=
(7y/9+⁹⁾2y)/(3·7y/9+⁹⁾y)=
(7y/9+18y/9)/(21y/9+9y)=
(25y/9)/(30y/9)=
25y/9·9/30y=25y/30y=(25/30)⁽⁵=5/6
__________________
x/2=y/5=>x=2y/5
(7x-2y)/(x+4y)=
(7·2y/5-⁵⁾2y)/(2y/5+⁵⁾4y)=
(14y/5-10y/5)/(2y/5+20y/5)=
(4y/5)/22y/5)=4y/5·5/22y=(4/22)⁽²=2/11
___________________-
x/3=y/11=>x=3y/11
(10x-y)/(x+y)=
(10·3y/11-¹¹⁾y)/(3y/11+¹¹⁾y)=
(30y/11-11y/11)/(3y/11+11y/11)=
(19y/11)/(14y/11)=19y/11·11/14y=19/14
