已知2/a=3/b=4/c,求分式a+b+c/3a-2b+c的值

题目

已知2/a=3/b=4/c,求分式a+b+c/3a-2b+c的值

答案

令2/a=3/b=4/c=1/t
则a=2t b=3t c=4t
(a+b+c)/(3a-2b+c)
=(2t+3t+4t)/(3×2t-2×3t+4t)
=9t/4t
=9/4