As a singer and_____actress,the star leads a busy life.

As a singer and_____actress,the star leads a busy life.
为什么横线上不填?

因为singer和actress在这里指的是同一个人——the star,（通过后面的leads三单形式可看出是同一个人.）一人身兼二职,主谓一致,所以两个名词singer和actress共用一个冠词a,所以actress前面不填冠词.
下面两个句子分别翻译为：
As a singer and actress,the star leads a busy life.
作为一个歌手兼演员,这个明星过着忙碌的生活.
As a singer and an actess,the stars lead a busy life.
作为歌手和演员（意指有的是歌手,有的是演员,不是一人兼职）,这些明星过着忙碌的生活.