X/3=Y/2=Z/5,则分式xy+xz+yz/x^2+y^2+z^2=

X/3=Y/2=Z/5,则分式xy+xz+yz/x^2+y^2+z^2=
X/3=Y/2=Z/5,则分式xy+xz+yz/x^2+y^2+z^2=

X/3=Y/2=Z/5,则分式xy+xz+yz/x^2+y^2+z^2=
设X/3=Y/2=Z/5=k
则x=3k,y=2k,z=5k
xy+xz+yz/x^2+y^2+z^2
=(6k^2+15k^2+10k^2)/(9k^2+4k^2+25k^2)
=(6+15+10)/(9+4+25)
=31/38

是求(xy+xz+yz)/(x^2+y^2+z^2)的值吧。
典型的一道题目：分子分母未知数乘积的幂次数相同。
令X/3=Y/2=Z/5=k
则，X=3K,Y=2K,Z=5K,
依次代入目标方程，
即(xy+xz+yz)/(x^2+y^2+z^2)
=(6K^2+15K^2+10K^2)/(9K^2+4K^2+25K^2)
=31/38