已知x/3=y/5=z/6,求3x-2y+z/2x+y+2z的值

题目

已知x/3=y/5=z/6,求3x-2y+z/2x+y+2z的值

答案

设x/3=y/5=z/6=k.
则:x=3k,y=5k,z=6k.
故原式=(3*3k -2*5k +6k)/(2 *3k + 5k + 2*6k)
=(9k -10k +6k) /(6k +5k +12k)
=5k/(23k)
=5/23