verb
BAD : The question is whether doctors should lengthen life when there is no hope of recovery.
GOOD : The question is whether doctors should prolong life when there is no hope of recovery.
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lengthen = make something longer; become longer: 'We can use the old curtains, but they'll have to be lengthened.' 'As evening fell, the shadows lengthened.'
prolong = prevent a feeling, activity or life from ending: 'He asked her another question just to prolong the conversation.'