已知|a|≠|b|，m＝|a|−|b||a−b|，n＝|a|+|b||a+b|，则m与n的大小关系．

Question

已知|a|≠|b|，m＝(|a|−|b|)/(|a−b|)，n＝(|a|+|b|)/(|a+b|)，则m与n的大小关系______．

Answer 1

ab＜0时，m＝(|a|−|b|)/(|a−b|)≤1，n＝(|a|+|b|)/(|a+b|)＞1所以m＜n
ab＞0时，若|a|＞|b|时m＝(|a|−|b|)/(|a−b|)＝1，n＝(|a|+|b|)/(|a+b|)＝1
若|a|＜|b|时，m＝(|a|−|b|)/(|a−b|)＝−1，n＝(|a|+|b|)/(|a+b|)＞1
综上m≤n
故答案为：m≤n