仕事が忙しくて

今日は仕事が忙しくてお昼を食べる暇がなかった。

I was so busy with work today that I didn't have time to eat lunch.

いるけれど父にはほとんど会えないし母は仕事が忙しくてあまり一緒にいられない

I have a father, but I hardly ever see him, and my mother is busy with work, so I can’t spend much time with her.

— Arrietty (2010)

仕事が忙しくて大変だ。

Work is so busy and exhausting.

仕事が忙しくて、君に手紙を書くひまがなかった。

I was too busy with work to find time to write you a letter.

仕事が忙しくて寝不足だって

They say they're sleep-deprived because work has been keeping them busy.

— PERFECT BLUE (1998)