若3/x=2/y=5/z,则x/3=y/2=z/5,设x/3=y/2=z/5=K,则x=3K,y=2K,z=5K
将其代入上式,得
6k2+10k2+15k2 31k2
-------------------- = ---------------= 31/38
9k2+4k2+25k2 38k2