已知(x,y>0,dfrac{1}{x}+dfrac{2}{y}=1),求(dfrac{1}{x+1}+dfrac{2}{y+1})的最大值_____
解答：令(a=dfrac{1}{x},b=dfrac{2}{y})则(a,b>0,a+b=1)
(dfrac{1}{x+1}+dfrac{2}{y+1}=dfrac{a}{a+1}+dfrac{2b}{b+2}=3-(dfrac{1}{a+1}+dfrac{4}{b+2})le 3-dfrac{9}{a+b+3}=dfrac{3}{4})
评论:做一个代换，把条件变简单，通过化简，要求的部分变成了我们熟悉的题型.