An idiom meaning to lose one's temper or patience — to become exasperated or fed up.
子供のいたずらが続いて、母親はとうとう業を煮やして叱った。
The child's pranks continued and the mother finally lost her temper and scolded him.
客が理不尽な要求を続けたので、店員も業を煮やして対応を止めた。
Because the customer kept making unreasonable demands, the clerk grew exasperated and stopped serving them.
説明を何度しても理解してくれないので、彼は業を煮やした。
He lost his patience after explaining it several times and still not being understood.