一道数学题：若x:y:z=2:3:4,求分式x-y-z /2x+3y的值若x:y:z=2:3:4,求分式x-y-z /2x+3y的值

一道数学题：若x:y:z=2:3:4,求分式x-y-z /2x+3y的值
若x:y:z=2:3:4,求分式x-y-z /2x+3y的值

令x=2a,y=3a,z=4a,
于是x-y-z /2x+3y = (-5a)/(13a) = -5/13

x:y:z=2:3:4
x/2 =y/3=z/4 =k
=>
x=2k , y=3k, z=4k
(x-y-z) /(2x+3y)
=(-5k)/(13k)
=-5/13

设x=2a，y=3a，z=4a
原式=(2a-3a-4a)/(2*2a+3*3a)=-5a/13a=-5/13