verb
BAD : They spent the whole night fighting against the fire.
GOOD : They spent the whole night fighting the fire.
BAD : Why were the boys fighting against each other?
GOOD : Why were the boys fighting each other?
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When you are talking about an event or something that lasts only a short time, use fight sb/sth (WITHOUT against ): 'He said he would fight anyone who tried to stop him.' 'The best way to fight a cold is to get plenty of sleep.'
You can use either fight sb/sth or fight against sb/sth when you are talking about a long struggle to overcome things such as poverty, disease, injustice or oppression: 'The ANC has spent half a century fighting (against) racism.' 'The group was founded in 1983 to fight (against) the military regime.'