已知x/2=y/3=z/4,求(xy+2yz-3xz)/(x^2+y^2+z^2)?

已知x/2=y/3=z/4,求(xy+2yz-3xz)/(x^2+y^2+z^2)?
已知x/2=y/3=z/4,求(xy+2yz-3xz)/(x^2+y^2+z^2)?

已知x/2=y/3=z/4,求(xy+2yz-3xz)/(x^2+y^2+z^2)?
设x/2=y/3=z/4=t,则x=2t,y=3t,z=4t,
所以(xy+2yz-3xz)/(x^2+y^2+z^2)
=(6t^2+24t^2-24t^2)/(4t^2+9t^2+16t^2)
=6/29.