Question

已知2m-3n/3m+n=2,求4m-6n/9m+3n+18m+6n/4m-6n的值

Answer 1

已知(2m-3n)/(3m+n)=2，所以(4m-6n)/(9m+3n)=2/3*(2m-3n)/(3m+n)=2/3*2=4/3
(18m+6n)/(4m-6n)=6/2*1/2=3/2
所以(4m-6n)/(9m+3n)+(18m+6n)/(4m-6n)=4/3+3/2=17/6
即(4m-6n)/(9m+3n)+(18m+6n)/(4m-6n)的值为17/6

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追问

为什么这么做

追答

题目给你的是2m-3n/3m+n=2
那么你必须把要求的转成已知量

Answer 2

4m-6n/9m+3n+18m+6n/4m-6n=3

Answer 3

4m-6n/9m+3n=(2/3)*(2m-3n/3m+n)=4/3
18m+6n/4m-6n=(6/2)*(3m+n/2m-3n)=3*(1/2)=3/2
最后4m-6n/9m+3n+18m+6n/4m-6n=4/3+3/2=17/6