at the expense of
US /æt ðə ɪkˈspens ʌv/
UK /æt ðə ɪkˈspens ʌv/

1.
à custa de, em detrimento de
resulting in harm or damage to (someone or something else)
:
•
He pursued his career at the expense of his family life.
Ele perseguiu sua carreira à custa de sua vida familiar.
•
The company increased profits at the expense of environmental regulations.
A empresa aumentou os lucros à custa das regulamentações ambientais.