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.
原文：https://www.cnblogs.com/mathstudy/p/8821213.html