to the detriment of
If something happens to the detriment of something or to a person's detriment, it causes harm or damage to them.
These tests will give too much importance to written exams to the detriment of other skills.
这些测试会太侧重于书面考核而不益于其他技能的培养。
without detriment to
If something happens without detriment to a person or thing, it does not harm or damage them.
These difficulties have been overcome without detriment to performance.
这些困难已经被克服了,且没有影响到表演。