Patience and endurance are highly regarded and highly rewarded values in Islam. To a person who does not believe in a hereafter this might sound like nonsense, but to one who does, euthanasia is certainly nonsense. La medicine en accusation - in Michel Solomon 'L' avenir de la vie', Coll. Les visages de L'avenir. This logic is completely alien to Islam.
Values take priority overprices.
Whether one or both of them attain old age in your life, say not to them a word of contempt but address them in terms of honor. Because such caring is a virtue ordained and rewarded by God in this world and in the hereafter, the believers don't take it as a debit but as an investment. When individual means cannot cover the needed care, it becomes, according to Islam, the collective responsibility of society, and financial priorities are reshuffled so that values take priority over pleasures, and people derive more pleasure from heeding values than from pursuing other pleasantries. A prerequisite of course is a complete moral and spiritual re-orientation of a society that does not hold to these premises. In an Islamic setting the question of euthanasia usually does not arise, and if it does, it is dismissed as religiously unlawful.