Question

Ajutor!!

Daca x/y=3/4, y =/= 0, atunci 2x+3y/4x+y
daca x/y=7=9, y =/= 0 atunci x+2y/3x+y
daca x/2=y/5 atunci 7x-2y/x+4y
daca x/3=y/11 atunci 10x-y/x+y

Answer 1

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