“粗率的处理”可以翻译为 "hasty or careless handling" 或 "rough and inattentive treatment"。
Hasty or careless handling 强调处理过程仓促或缺乏细心。
Rough and inattentive treatment 则侧重于粗暴和疏忽的态度。
根据具体语境，可以选择更贴切的表述。例如：
The issue was resolved with hasty handling, leading to further problems. （问题因处理仓促而进一步恶化。）
Such rough and inattentive treatment of historical artifacts is unacceptable. （对历史文物的这种粗率处理是不可接受的。）