X/3=Y/2=Z/5,则分式xy+xz+yz/x^2+y^2+z^2=

题目

X/3=Y/2=Z/5,则分式xy+xz+yz/x^2+y^2+z^2=

答案

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