Ta có : `x/3=y/4`
`⇒x/15=y/20` `(`chia mỗi vế cho `5)`
`y/5=z/6⇒y/20=z/24` `(`chia mỗi vế cho `4)`
`⇒x/15=y/20=z/24`
Đặt : `x/15=y/20=z/24=k`
`⇒x=15k;y=20k;z=24k` `(1)`
`⇒A={2x+3y+4z}/{3x+4y+5z}` `(2)`
Từ `(1)` và `(2), ⇒A={2.15k+3.20k+4.24k}/{3.15k+4.20k+5.24k}`
`⇒A={30k+60k+96k}/{45k+80k+120k}`
`⇒A={186k}/{245k}`
`⇒A=186/245`