若x/3=y/2=z/5,则分式xy+yz+zx/x²+y²+z²等于?

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

设x/3=y/2=z/5=k
则
x=3k，y=2k，z=5k
∴xy+yz+zx/x²+y²+z²
=(6k²+10k²+15k²)/(9k²+4k²+25k²)
=31k²/38k²
=31/38

运用换元法。
设x/3=y/2=z/5=k则有
x=3k
y=2k
z=5k
代入分式中，得
3k.2k+2k.5k+5k.3k/9k.k+4k.k+25k.k
=31k平方/38k平方
约去K平方
=31/38