已知式等价于(a-c)/(a-b)+2(a-c)/(b-c)≥m,
[(a-b)+(b-c)]/(a-b)+2[(a-b)+(b-c)]/(b-c)≥m,
3+(b-c)/(a-b)+2(a-b)/(b-c)≥m,
由均值不等式上式左≥3+2*2^(1/2),
所以m=3+2*2^(1/2).选A.